FRG Meeting 2017–

from quantum gravity and dark energyto ultracold atoms and condensed matter

IWH Heidelberg, Hauptstraße 242, Heidelberg

March 7 – March 10, 2017

Contents

1 Programme 3

2 General Information 5

3 Talks: Titles & Abstracts 9

4 Posters: Titles & Abstracts 20

5 List of participants 31

1

Tuesday 7th Wednesday 8th Thursday 9th Friday 10th

8:50 – 9:00 Christof Wetterich IWH Greeting

9:00 – 9:40

Holger Gies

Renormalization flow

of fermionic systems

Ronny Thomale

History, Present, Future: Functional RG

for unconventional superconductors

Jens Braun

Ground-state properties of spin- and

mass-imbalanced Fermi gases

Sebastian Diehl

Fate of Kosterlitz-Thouless Physics

in Driven Open Quantum Systems

9:40 – 10:20

Carsten Honerkamp

Truncated unity fRG on square

and honeycomb lattices

Laura Classen

Phase transitions and critical behavior

in 2D Dirac materials

Igor Boettcher

Anisotropy induces non-Fermi liquid behavior and

nemagnetic order in 3D Luttinger semimetals

Dominique Mouhanna

Statistical physics

of polymerized membranes

10:20 – 10:50 Coffee break Coffee break Coffee break Coffee break

10:50 – 11:30

Stefan Lippoldt

Quantum gravity and

Standard-Model-like fermions

DiscussionsMisha Shaposhnikov

TBA

Roberto Percacci

The Ward identity of

scale transformations

11:30 – 12:10

Léonie Canet

Correlation functions in homogeneous

and isotropic turbulence

Francesco Sannino

Exact Nonperturbative results

for Asymptotic (Un)Safety

Nikos Tetradis

Effective Description of Dark Matter

as a Viscous Fluid

Frank Saueressig

Asymptotic Safety and the Arnowitt-

Deser-Misner formulation of gravity

12:10 – 14:30 Lunch break Lunch break Lunch break Lunch break

14:30 – 15:10

Bertrand Delamotte

Bound states in the

three-dimensional φ4 model

Sri Raghu

Two dimensional metallic phases

from disordered QED3

Daniel Litim

From exact asymptotic safety

to physics beyond the Standard Model

Steven Mathey

KPZ dynamics with correlated noise:

Emergent symmetries and non-universal observables

Nicolas Wink

Real time correlation functions at finite temperature

15:10 – 15:40 Coffee break Coffee break Coffee break

Jean-Paul Blaizot

Remarks on the 2PI formalisms

and the functional RG

15:40 – 16:20

Nicolas Dupuis

Thermodynamics and transport

near a quantum critical point

Nicolai Christiansen

Interplay of gravity and gauge theories

at the Planck scale

Julien Serreau

NPRG techniques for quantum scalar fields

in de Sitter space

Closing 15:50 – 16:00

16:20 – 17:00Stefan Flörchinger

Effective dissipation

Martin Reuter

Viability of the Asymptotic Safety scenario

beyond renormalizability?

Discussions

17:00 – 17:30 Snacks & resfreshments

17:30 – Poster flash (30min) & session 19:00 Conference dinner

2

Tuesday 7th Wednesday 8th Thursday 9th Friday 10th

8:50 – 9:00 C. Wetterich IWH Greeting

9:00 – 9:40 H. Gies R. Thomale J. Braun S. Diehl

9:40 – 10:20 C. Honerkamp L. Classen I. Boettcher D. Mouhanna

10:20 – 10:50 Coffee Coffee Coffee Coffee

10:50 – 11:30 S. Lippoldt Discussions M. Shaposhnikov R. Percacci

11:30 – 12:10 L. Canet F. Sannino N. Tetradis F. Saueressig

12:10 – 14:30 Lunch Lunch Lunch Lunch

14:30 – 15:10 B. Delamotte S. Raghu D. Litim Prize talk 1 & 2

15:10 – 15:40 Coffee Coffee Coffee J.-P. Blaizot

15:40 – 16:20 N. Dupuis N. Christiansen J. Serreau Closing 15:50

16:20 – 17:00 S. Flörchinger M. Reuter Discussions

17:00 – 17:30 Snacks

17:30 – Poster session 19: 00 Conference dinner

3

Chairs

Tuesday morning session: Jan Pawlowski

Tuesday afternoon session: Michael Scherer

Wednesday morning session: Gian Paolo Vacca

Wednesday afternoon session: Manfred Salmhofer

Thursday morning session: Alfio Bonnano

Thursday afternoon session: Thomas Gasenzer

Friday morning session: Tilman Enss

Friday afternoon session: Astrid Eichhorn

International poster prize committee

Léonie Canet (Université Grenoble Alpes)

Nicolas Dupuis (Université Pierre et Marie Curie)

Holger Gies (TPI Jena)

Roberto Percacci (SISSA, Trieste)

Srinivas Raghu (Stanford University)

4

2 General Information

Local contacts:

Astrid EichhornE-mail: eichhorn@thphys.uni-heidelberg.deCell: +49 177 71 193 31

Michael SchererE-mail: scherer@thphys.uni-heidelberg.deCell: +49 176 62 168 108

Conference dinner:

The conference dinner takes place in Haus Buhl, which isclose to the IWH, see on the map below.

Useful links:

FRG-Meeting Website:https://www.thphys.uni-heidelberg.de/~frg-meeting/

How to find the conference center (IWH):http://www.iwh.uni-hd.de/wegbeschreibung_engl.html

Hotel Vierjahreszeiten:http://www.4-jahreszeiten.de/hotel/en/

Institute for Theoretical Physics (Philosophenweg 16):https://www.thphys.uni-heidelberg.de/

5

For dinner

Heidelberg’s old town has a lot of very nice restaurants andbars. Please, ask the locals for more recommendations. Thefollowing list of hints is not exhaustive!

SchnitzelhausNeckarmünzgasse 10, 240m from IWHKulturbrauereiBrewery, Leyergasse 6, 250m from IWHGasthaus Weisses RösselHauptstraße 210, 350m from IWHWirtshaus NepomukObere Neckarstraße 2, 550m from IWH

For drinks et al.

Bent BarCocktails, Leyergasse 2, 270m from IWHKulturbrauereiBrewery, Leyergasse 6, 250m from IWHMarstallcafé HeidelbergStudent’s Café, Marstallhof 1, 950m from IWHCave 54Jazz Club, Krämergasse 2, 550m from IWHDestilleUntere Str. 16, 700m from IWHLa Fée Bar CaféCocktails, Untere Str. 29, 650m from IWH

Generally, you can try Untere Straße, 500m from IWH!

6

Map of Heidelberg’s old town:

25/02/2017 Internationales Wissenschaftsforum Heidelberg to Hotel Vier Jahreszeiten Heidelberg - Google Maps

https://www.google.de/maps/dir/Internationales+Wissenschaftsforum+Heidelberg,+Hauptstra%C3%9Fe,+Heidelberg/Hotel+Vier+Jahreszeiten+Heidelberg,+Haspelga... 1/1

Map data ©2017 GeoBasis-DE/BKG (©2009), Google 50 m

7 min600 m

via Hauptstraße and Obere Neckarstraße

8 min700 m

via Hauptstraße

8 min650 m

via Hauptstraße and Heiliggeiststraße

Walk 600 m, 7 minInternationales Wissenschaftsforum Heidelberg to HotelVier Jahreszeiten Heidelberg

7

IWH and Haus Buhl: location of conference dinner←↩

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3 Talks: Titles & Abstracts

Jean-Paul Blaizot (CEA Saclay) ←↩

Remarks on the 2PI formalisms and the functional RG

Igor Boettcher (SFU Vancouver) ←↩

Anisotropy induces non-Fermi liquid behavior and nemagneticorder in 3D Luttinger semimetals

We illuminate the intriguing role played by spatial anisotropyin three-dimensional Luttinger semimetals featuring quadraticband touching and long-range Coulomb interactions. For suf-ficiently strong anisotropy, two main effects come to light. First,the three-dimensional system features an Abrikosov non-Fermiliquid ground state. Second, qualitatively new fixed pointsshow up which describe quantum phase transitions into phaseswith nemagnetic orders – higher-rank tensor orders that breaktime-reversal symmetry, and thus have both nematic and mag-netic character. In real materials these phases may be re-alized through sufficiently strong microscopic short-range in-teractions. On the pyrochlore lattice, the anisotropy-inducedfixed points determine the onset of all-in-all-out or spin ice or-dering of local magnetic moments.

Jens Braun (TU Darmstadt) ←↩

Ground-state properties of spin- and mass-imbalanced Fermigases

9

Michael Buchhold (University of Cologne) ←↩

Nonstandard universality and scaling regimes by rare eventsin weakly disordered Dirac metals

A unified theory for weakly disordered three-dimensional Diracmetals is provided based on the supersymmetry approach. Itincorporates simultaneously both rare instanton events andthe effect of long wavelength electron fluctuations in a fre-quency resolved manner. The presence of an instanton back-ground and associated a spontaneous breakdown of super-symmetry destabilizes the previously known supersymmet-ric critical fixed point, and gives rise to a new infrared stablefixed point characterizing a different, novel universality class.The new fixed point governs physical observables in an in-termediate frequency window, which is located in between aninstanton-dominated and a supersymmetric scaling regime,and whose size may depend on the observable under consid-eration.

Leonie Canet (LPMMC, Université Grenoble Alpes) ←↩

Correlation functions in homogeneous and isotropic turbulence

Turbulence is an ubiquitous phenomenon in natural and in-dustrial flows. Yet, calculating its statistical properties, andin particular what is generically called intermittency effects,that is violations of standard scale invariance, remains an un-solved issue. In this talk, I will focus on isotropic and homoge-neous turbulence in three-dimensional incompressible flows.I will explain how one can derive closed FRG flow equations,which are exact in the limit of large wave-numbers, for the

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two-point, and more generally n-point, correlation functions ofthe turbulent stationary state. I will present the full space timedependent fixed point solution of these equations for the two-point function, and show that it encompasses intermittencyeffects. These predictions are compared to results from directnumerical simulation of Navier-Stokes equations and experi-mental results, showing a remarkable agreement.

Nicolai Christiansen (ITP Heidelberg) ←↩

Interplay of gravity and gauge theories at the Planck scale

I study the coupling of gauge theories to quantum gravity. Ageneral mechanism how graviton fluctuations induce higherorder operators in the gauge sector is discussed. It is shownhow asymptotically safe gravity can cure the triviality prob-lem in Abelian gauge theories and the status of asymptoticfreedom and asymptotic safety in non-Abelian gauge theoriescoupled to gravity is investigated.

Laura Classen (BNL Brookhaven) ←↩

Phase transitions and critical behavior in 2D Dirac materials

We study the quantum phase transitions occurring in low-dimensional Dirac materials for sufficiently large interactionsat the example of a spin and a charge density wave, and aKekulé bond order. We describe these systems by effectiveGross-Neveu-Yukawa theories with order parameter fields ofdifferent symmetry. The spin and charge density waves arecharacterised by an O(3) or Z2 field, respectively. The Kekuléorder displays a more exotic Z3 symmetry. With the help of a

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functional RG approach, we determine the nature of the corre-sponding phase transitions and give estimates for the criticalexponents in case of continuous transitions. The fixed pointstructure and its stability properties thereby strongly dependon the number of Dirac fermions. The coupling of the differentorder parameters induces multicritical behavior and describesthe phase diagram in the vicinity of the point, where differentsymmetry-broken phases meet. This allows us to investigatethe competition of spin and charge density waves as expectedfor equivalent interactions strengths in these channels.

Bertrand Delamotte (Université Pierre et Marie Curie) ←↩

Bound states in the three-dimensional φ4 model

Sebastian Diehl (Cologne University) ←↩

Fate of Kosterlitz-Thouless Physics in Driven Open QuantumSystems

Recent developments in diverse areas – ranging from coldatomic gases to light driven semiconductors to microcavityarrays – move systems into the focus which are located onthe interface of quantum optics, many-body physics and sta-tistical mechanics. They share in common that coherent anddriven-dissipative quantum dynamics occur on an equal foot-ing, creating genuine non-equilibrium scenarios without im-mediate counterpart in equilibrium condensed matter physics.We study such systems in two dimensions on the basis of aduality transformation mapping the problem into a non-linearnoisy electrodynamics, where the charges represent vortices.In the absence of vortices, the problem is equivalent to the

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Kardar-Parisi-Zhang equation. We show that the paradig-matic quasi-long range order of equilibrium systems at lowtemperature must be absent asymptotically. More precisely,the non-equilibrium drive generates two independent scales,leading to distinct but subalgebraic behavior of the asymptoticcorrelation functions. Although the usual Kosterlitz-Thoulessphase transition does thus not exist out of equilibrium, a newphase transition into a vortex turbulent state is found, whichoccurs as a function of increasing non-equilibrium strength.

Nicolas Dupuis (Université Pierre et Marie Curie) ←↩

Thermodynamics and transport near a quantum critical point

We discuss the application of non-perturbative functional renor-malization group (FRG) to the relativistic quantum O(N) modelin two space dimensions. This model describes the criticalregime of many condensed-matter systems including quan-tum antiferromagnets and the superfluid–Mott-insulator tran-sition of bosons in an optical lattice. We discuss both theuniversal equation of state (which, thanks to the quantum-classical mapping, can be compared with Monte Carlo simu-lations of classical 3D systems in a finite geometry) and thezero-temperature conductivity. The universal value of the lat-ter at the quantum critical point is in good agreement withquantum Monte Carlo estimates and conformal bootstrap re-sults. In the ordered phase, we find that the conductivity hasa "super-universal" component which is independent of boththe distance to the quantum critical point and the value of N.

Stefan Flörchinger (ITP Heidelberg) ←↩

13

Effective dissipation

I will discuss how effectively dissipative dynamics can arise inquantum field theories, why this is interesting from an informa-tion theoretic point of view and how understanding these phe-nomena in more detail could help to solve some interestingopen problems in cosmology and condensed matter physics.

Holger Gies (TPI Jena) ←↩

Renormalization flow of fermionic systems

We review the present status of functional renormalizationgroup applications to low dimensional relativistic fermion sys-tems. We report on quantitative progress within systematicand consistent approximation schemes, highlight new con-ceptual aspects, and discuss open questions and puzzles.

Carsten Honerkamp (RWTH Aachen) ←↩

Truncated unity fRG on square and honeycomb lattices

Recently the truncated-unity functional renormalization group(TUfRG) has been put forward as a systematic technique fortreating the evolving structure of the four-point vertex in inter-acting many-fermion systems on the lattice. It incorporatesprevious channel-decomposition approaches and allows foran efficient evaluation by parallel computing. We present re-sults of first studies on square and honeycomb lattices. Wealso describe how the now-achieved momentum resolutioncan be employed to study correlation functions and the effectof longer-range interactions in more detail.

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Stefan Lippoldt (ITP Heidelberg) ←↩

Quantum gravity and Standard-Model-like fermions

We discover that chiral symmetry does not act as an infraredattractor of the renormalization group flow under the impactof quantum gravity fluctuations. Thus, observationally viablequantum gravity models must respect chiral symmetry. Inour truncation, asymptotically safe gravity does, as a chiralfixed point exists. A second non-chiral fixed point with mas-sive fermions provides a template for models with dark mat-ter. This fixed point disappears for more than 10 fermions,suggesting that an asymptotically safe ultraviolet completionfor the standard model plus gravity enforces chiral symmetry.

Daniel Litim (University of Sussex) ←↩

From exact asymptotic safety to physics beyond the StandardModel

The concept of an interacting UV fixed point in quantum fieldtheory is of high interest per se; for particle physics it opensup theory space for model building. In this talk, we discusstheorems and exact results for asymptotic safety in general4d gauge theories weakly coupled to matter. The pivotal roleof Yukawa interactions is highlighted. Minimal asymptoticallysafe extensions of the Standard Model are put forward andtheir signatures at colliders (such as R-hadrons, diboson sig-natures, the evolution of the strong and weak coupling con-stants) are worked out.

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Dominique Mouhanna (Université Pierre et Marie Curie)←↩

Statistical physics of polymerized membranes

The physics of polymerized membranes has known a renewedinterest due to the fact that novel carbon materials like grapheneare, as for their elastic properties, very well described by thesesystems. Thus for practical considerations, notably designof novel materials with outstanding graphene-like mechan-ical, optical or electronically properties, as well as from amore fundamental point of view, a well controlled descriptionof these systems is highly needed. Physical, i.e. two dimen-sional, polymerized membranes are from the field theoreti-cal point of view strongly interacting systems whose qualita-tive and quantitative analysis call for efficient tools like self-consistent screening approximation or nonpertubative renor-malization group. I show in my talk how these techniques al-low to describe various physical effects taking in place in clas-sical or quantum, pure or disordered, isotropic or anisotropic,membranes.

Roberto Percacci, (SISSA, Trieste) ←↩

The Ward identity of scale transformations

The arbitrariness of the background-quantum split gives riseat the classical level to a shift symmetry. I will derive the Wardidentities for a subclass of such shift transformations, namelythose where the background and fluctuation fields are sub-jected to a scale transformation. The Ward identity can besolved together with the flow equation, reducing the numberof arguments in the Effective Average Action.

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Srinivas Raghu (Stanford University) ←↩

Two dimensional metallic phases from disordered QED3

With few exceptions, the existence of 2d metallic phases atzero temperature requires electron-electron interactions. Con-sequently, experimental observations of such metallic behav-ior have largely defied explanation. We show that (2+1)Dquantum electrodynamics (QED3) with a large, even numberof fermion flavors remains metallic in the presence of weakscalar potential disorder due to the dynamic screening of dis-order by gauge fluctuations. We also show that QED3 withweak mass disorder is governed by a stable fixed point withfinite disorder and interaction strengths.

Martin Reuter (Mainz University) ←↩

Viability of the Asymptotic Safety scenariobeyond renormalizability?

An acceptable quantum field theory of gravity and spacetimegeometry must comply with a number indispensable physicalprinciples such as Hilbert space positivity and background in-dependence in addition to (nonperturbative) renormalizability.We discuss some of them in a simplified two-dimensional set-ting where the tools of conformal field theory are available.

Francesco Sannino (DIAS, CP3) ←↩

Exact Nonperturbative results for Asymptotic (Un)Safety

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Frank Saueressig (Nijmegen) ←↩

Asymptotic Safety and the Arnowitt-Deser-Misner formulationof gravity

I will review recent progress on formulating and evaluatinggravitational renormalization group flows in the presence ofa foliation structure of spacetime. The foliation gives rise to apreferred direction which may naturally play the role of time ina Lorentzian setting. In this talk, I will contrast the fixed pointstructures and phase diagrams arising from the renormaliza-tion group flows in the covariant and foliated settings andpresent first results on the inclusion of matter fields in the fo-liated setting. The relevance of the construction for the CausalDynamical Triangulations program, Horava-Lifshitz gravity, andcosmological fluctuation spectra will be discussed.

Julien Serreau (Université Paris Diderot) ←↩

NPRG techniques for quantum scalar fields in de Sitter space

I review recent developments concerning the use of NPRGtechniques for describing the nontrivial infrared regime of lightscalar fields in de Sitter space. Long wavelength fluctuations(in units of the spacetime curvature) undergo a dramatic grav-itational amplification which is responsible for dramatic phe-nomena, such as the radiative restoration of spontaneouslybroken symmetries.

Misha Shaposhnikov (EPF Lausanne) ←↩

TBA

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Nikos Tetradis (University of Athens) ←↩

Effective Description of Dark Matter as a Viscous Fluid

Ronny Thomale (Würzburg University) ←↩

History, Present, Future: Functional RG for unconventionalsuperconductors

Functional renormalization group has become a fundamen-tal element of contemporary methods in condensed matter toidentify Fermi surface instabilities. Among them, unconven-tional superconductivity has triggered particular importance,where the methodological edge of FRG against e.g. ran-dom phase approximation has revealed itself in different ma-terial contexts such as iron pnictides, strontium ruthenate, andmany more. I will give a review on promising current topicaldirections of unconventional superconductors where the fRGpromises to be of particular use.

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4 Posters: Titles & Abstracts

Anton Cyrol (ITP Heidelberg) ←↩

Yang-Mills Correlation Functions at Finite Temperature

We calculate Landau gauge Yang-Mills correlation functionsat finite temperature with the functional renormalization group.Our self-consistent computation fully includes the splitting intomagnetic and electric components of the gluon propagatorand the classical tensor structures, but is limited to zerothmode correlation functions. In the limit of zero temperature,the results of our parameter-free computation converge to thevacuum results from arXiv:1605.01856 [hep-ph].

Tobias Denz (ITP Heidelberg) ←↩

Towards apparent convergence in asymptotically safe quan-tum gravity

The asymptotic safety scenario in gravity is accessed withinthe systematic vertex expansion. In the present work this ex-pansion scheme is extended to the dynamical graviton four-point function. For the first time, this provides us with a closedflow equation for the graviton propagator: all vertices andpropagators involved are computed from their own flows. Interms of a covariant operator expansion the current approx-imation gives access to Λ, R, R2 as well as R2

µν and higherderivative operators. We find a UV fixed point with three at-tractive and two repulsive directions, thus confirming previousstudies on the relevance of the first three operators. In the in-frared we find trajectories that correspond to classical general

20

relativity and further show non-classical behaviour in somefluctuation couplings. We also find signatures for the appar-ent convergence of the systematic vertex expansion. Thisopens a promising path towards establishing asymptoticallysafe gravity in terms of apparent convergence.

Aaron Held (ITP Heidelberg) ←↩

Constraining quantum gravity by recovering the Standard Model

We propose a scenario to constrain the couplings of a quan-tum field theory of gravity. We assume that such a theory in-corporates both gravity and matter degrees of freedom. Renor-malization group flows connect the high energy scale directlywith physics at the electroweak scale under the assumptionthat no new physics exists at intermediate scales. We discusshow the requirement of recovering the correct low-energy limitin the matter sector could constrain the gravitational parame-ter space. Specifically, we explore constraints on the gravita-tional couplings arising in a simple Higgs-Yukawa model.

Bernhard Ihrig (ITP Heidelberg) ←↩

Critical behavior of Dirac materials:Gross-Neveu-Yukawa model at three loops

Dirac and Weyl fermions appear as quasi-particle excitationsin many condensed-matter systems. They display variousquantum transitions which fall into the universality class of theGross-Neveu model. We study its bosonized version – theGross-Neveu-Yukawa model – at three-loop order and cal-culate critical exponents in D = 4 − ε. The comparison to

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other approaches, namely FRG and Monte Carlo methods,paves the road to a more comprehensive understanding ofthis paradigmatic example of interacting QFTs. We discussapplications of the results for the metal-insulator transitionin graphene and the disorder-induced quantum transition inWeyl semimetals.

Benjamin Knorr (TPI Jena) ←↩

Towards a local potential approximation in quantum gravity

We show how to calculate the renormalization group flow ofcorrelation functions in quantum gravity to arbitrary power ofthe fluctuation field. The new approach thus for the first timeallows to resolve arbitrarily strong fluctuations and an infinitenumber of fluctuation couplings. It also allows for a check ofthe apparent convergence of the vertex expansion.

Ken Kikuchi (Nagoya University) ←↩

On three-dimensional trace anomalyfrom holographic local RG

Odd-dimensional quantum field theories (QFTs) can have non-zero trace anomalies if external fields and the Levi-Civita ten-sor are supplied, which are needed to construct Lorentz sin-glets with appropriate mass dimensions (or weights). Wehave studied a three-dimensional QFT and explicitly computedthe trace of the stress tensor using the holographic (local)renormalization group (RG). We have checked that our resultreproduce all known properties of vector beta functions andthe Wess-Zumino consistency condition. However, we found

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the anomalies are proportional to beta functions, and the tracevanishes on fixed points. We clarify what is responsible for thevanishing trace anomalies.

Steven Mathey (University of Cologne) ←↩

Non-Equilibrium interface dynamics with correlated noise:Emergent symmetries and non-universal observables

In this contribution I investigate the physics of a 1D KPZ inter-face that is subjected to a noise with smooth spatio-temporalcorrelations. This problem was previously studied numericallyas well as with the Replica Trick in a Gaussian variational ap-proach. It was found that the small scale features depend onthe details of the microscopic noise while (up to the overallamplitude factors) the exact solution with white noise governsthe large scales. In the present work, Functional Renormal-ization Group (FRG) methods are employed in order to re-solve the non-perturbative features of KPZ dynamics. TheFRG makes it possible to follow the renormalization groupflow from its initial conditions all the way down to its fixedpoint. I show that the exact solution emerges on large scalesindependently of the details of the noise correlations. More-over the small scale features (and their dependence on theparticular choice of the noise correlations) are resolved andcompared to direct numerical simulations.

Jordi Paris-Lopez (University of Graz) ←↩

Properties of Bound States using the FRG

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Dyson-Schwinger, Bethe-Salpether and Faddeev equationshave long provided a functional way of deriving propertiesof bound states for many different systems. Given the com-plexity and numerical challenge associated to the mentionedequations, the FRG was suggested as an alternative func-tional method to study bound states. As a first step, prop-erties of the bound states are to be analysed in the Quark-Meson model. Solutions to the flow equations of momentumdependent n-point functions and techniques, such as dynam-ical hadronization and analytical continuation using modifiedregulators, need to be under control in this model before work-ing in QCD. A few examples and preliminary results will beshown.

Martin Pospiech (TU Darmstadt) ←↩

A Fierz-complete NJL model study: fixed points and phasestructure at finite temperature and density

Manuel Reichert (ITP Heidelberg) ←↩

Quantum Gravity with a vertex expansion on curved back-grounds

We investigate the phase diagram of quantum gravity within avertex expansion about constantly curved backgrounds. Weevaluate the graviton two-point and three-point function with aspectral sum on a sphere and obtain UV fixed point functionsµ∗(R), λ∗3(R) and g∗(R). The existence of these UV fixed point

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functions gives further evidence for the asymptotic safety sce-nario. We further investigate the effect of these UV fixed pointfunctions on the background potential. Here we find a solutionto the equation of motion for small curvature.

Mahmoud Safari (INFN) ←↩

Covariant and background-independent functional renormal-ization in scalar QFT.

In the context of scalar QFT we introduce a class of generi-cally nonlinear quantum-background splits for which the split-ting Ward identity, encoding the single-field dependence in theeffective action, can be solved exactly. We show that, by ap-propriate choice of cutoff, this can be used to construct an ef-fective average action which is both covariant and dependenton the background and fluctuation fields only through a singletotal field in a way independent from the dynamics. Moreoverwe discuss the criteria under which the ultraviolet symmetriesare inherited at lower scales.

Giulio Schober (RWTH Aachen) ←↩

Response Theory of the Electron-Phonon-Coupling

We present a systematic theoretical enquiry concerning theconceptual foundations and the nature of phonon-mediatedelectron-electron interactions. Starting from the fundamen-tal many-body Hamiltonian, we propose a simple scheme todecouple the electrons and nuclei of a crystalline solid viaeffective interactions. These effective interactions, which weexpress in terms of linear response functions, are completely

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symmetric between electrons and nuclei. Correspondingly,we derive concrete formulae for both the effective electron in-teraction mediated by phonons and the effective nuclear inter-action mediated by electrons. In particular, we rederive fromour fundamental ansatz the well-known general expressionsof the effective electron-electron interaction in terms of theelastic Green function and the phonon dispersion relation. Wefurther show that the effective nuclear interaction coincides inthe instantaneous limit with the dynamical matrix as calcu-lated in electronic structure theory. If combined with the Kuboformalism, our general formulae lend themselves to the calcu-lation of effective interactions from first principles. By showingthe compatibility of our approach with the functional integralformalism, this work also paves the way for the derivation ofab initio initial interactions for functional renormalization groupapplications.

Davide Squizzato (Université Grenoble Alpes) ←↩

KPZ equation for disordered out-of-equilibrium quantum sys-tems coupled to a thermal bath

In the last few years experimental progress in the area ofout-of-equilibrium exciton-polariton gases gave rise to sev-eral questions concerning the physical behaviour of Bose-Einsten condensates under pump and dissipation. Such sys-tems can be theoretically described by a generalised Gross-Pitaevskii Equation (gGPE) in which complex coefficients andnoise enrich the equilibrium picture. An analytical mappingbetween gGPE and the Kardar-Parisi-Zhang (KPZ) equationhas been demonstrated at long wavelength if the fluctuations

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of the amplitude of the condensate are negligible with re-spect to the ones of the phase field. Hence one expectsthat the long-distance properties of driven-dissipative conden-sates belong to the KPZ universality class and a numericalproof was given in (1+1)D. However an experimental obser-vation of such mapping is still missing. An important featureof experimental set-up is the presence of unavoidable disor-der due to cavity imperfections and phonons. In this work wedevelop a Keldysh field-theoretical approach taking into ac-count the role of disorder and interactions with an externalphonon-reservoir at thermal equilibrium; on the one hand wederive the gGPE-KPZ mapping and perform numerical simu-lations of the gGPE to test our predictions, on the other handthe field-theoretical approach can serve as a basis for a futureFunctional-Renormalization-Group treatment.

Imola Steib (University of Debrecen) ←↩

Renormalization of bilocal potentials

The functional renormalization group (RG) method is one ofthe most important nonperturbative tools in quantum theory,enabling the removal of the degrees of freedom or modes ofa physical system successively. In the traditional RG techni-que, the blocking transformation takes into account the con-tributions of the pure states only. Using the closed time path(CTP) formalism the RG method can be generalized to takeinto consideration the contribution of the mixed states, as well.This description can even account for the entanglement be-tween the infrared (IR) and the ultraviolet (UV) modes (S.

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Nagy, J. Polonyi, I. Steib, Quantum renorma- lization group,Phys.Rev. D 93 (2016), 025008). The interaction betweenthe UV and IR modes requires the vertices to carry finite mo-menta. Consequently, a bilocal potential has to be introducedinto the action. Thus, the new couplings become momentumdependent. We use the Wegner-Houghton equation whichdescribes the evolution of the Wilsonian action. Due to thesharp cutoff, the equation cannot ac- count for the higherorder terms in the gradient expansion. However, the inclu-sion of the bilocal potential provides a more general treatmentin this respect. The traditional RG treatment of Euclideanaction containing a bilocal potential is highly nontrivial. Wedetermined the leading order, tree level evolution equationfor the potential for a 3 dimensional one- component scalarmodel, and calculated the evolution of the momentum depen-dent couplings. Generally, the couplings cor- responding tothe quadratic and quartic terms in the local action. How-ever, we found a new relevant momentum dependent cou-pling, which belongs to the bilocal potential. The relevantcouplings determine which interactions are important in thephysical model, therefore their knowledge is necessary for theproper description of the system. Our results show that thetraditionally used local potential in the RG method may not besuitable to find all the relevant interactions in the model, andthe evolution of the bilocal potential has to be determined, aswell.

Malo Tarpin (Université Grenoble Alpes) ←↩

Exact flow equations for high order correlation functions infully developed turbulence

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To give a complete statistical description of isotropic fully de-veloped turbu- lence is a longstanding issue of classical physics,which has seen few progresses since the pioneering workof Kolmogorov in 1941. Recently, a decisive step has beenmade in this direction. Using non-perturbative renormaliza-tion group (NPRG) and newly discovered symmetries, a closedow equation for the two- point correlation function, which is ex-act in the large momentum limit, has been derived. This owequation exhibits a very peculiar feature, which is non- de-coupling between the large and small scales. This propertyis the hallmark of physics beyond the theory of Kolmogorov.In the present work, we extend this result to arbitrary ordercorrelation functions, that is we show that the ow of any ordercorrelation functions can be closed exactly in the large mo-mentum limit using symmetries. We deduce from this resultnew predictions for their behavior and we discuss its conse-quence on the structure functions.

Fleur Versteegen (ITP Heidelberg) ←↩

An asymptotically safe gauge coupling

In the search for a fundamental theory of quantum gravity andmatter, we use non-perturbative functional RenormalizationGroup methods to examine a system composed of a chargedscalar and a U(1) gauge field, coupled to asymptotically safequantum gravity. Preliminary results for the flow of the gaugecoupling show evidence for the existence of two fixed points.The most significant result is the irrelevant nature of the cou-pling at one of the fixed points, hinting towards the possibilityof predicting its value at low energies.

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Nicolas Wink (ITP Heidelberg) ←↩

Real time correlation functions at finite temperature

We present a first principle method to gain access to thegeneral momentum and frequency dependence of correlationfunctions at finite temperature. This allows us to use existingframeworks and workflows developed for Euclidean theorieswithin the FRG. We apply this method to the O(N) model inorder to extract the spectral functions of the pion and sigmameson for various temperatures across the phase transition.

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5 List of participants

1. Jean-Paul Blaizot, CNRS/UMR 3681, CEA Saclay2. Jürgen Berges, ITP Heidelberg3. Jens Braun, TU Darmstadt4. Igor Boettcher, Simon Fraser University, Vancouver5. Alfio Bonanno, INAF, Catania6. Michael Buchhold, University of Cologne7. Léonie Canet Canet, LPMMC, Université Grenoble Alpes8. Nicolai Christiansen, Heidelberg University9. Laura Classen, BNL Brookhaven

10. Olivier Coquant, Université Pierre et Marie Curie11. Anton Cyrol, ITP Heidelberg12. Bertrand Delamotte, Université Pierre et Marie Curie13. Nicolo Defenu, ITP Heidelberg14. Tobias Denz, ITP Heidelberg15. Sebastian Diehl, University of Cologne16. Nicolas Dupuis, Université Pierre et Marie Curie17. Astrid Eichhorn, ITP Heidelberg18. Tilman Enss, ITP Heidelberg19. Bruno Faigle-Cedzich, ITP Heidelberg20. Stefan Flörchinger, Heidelberg University21. Thomas Gasenzer, ITP Heidelberg22. Holger Gies, Jena University23. Maurits Haverkoort, ITP Heidelberg24. Aaron Held, ITP Heidelberg25. Markus Heller, ITP Heidelberg26. Carsten Honerkamp, RTWH Aachen University27. Bernhard Ihrig, ITP Heidelberg

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28. Ken Kikuchi, Nagoya University29. Tomotaka Kitamura, Waseda University30. Benjamin Knorr, TPI Jena31. Stefan Lippoldt, Heidelberg University32. Daniel Litim, University of Sussex33. Johannes Lumma, ITP Heidelberg34. Stephen Mathey, University of Cologne35. Walid Ahmed Mian, ITP Heidelberg36. Luminita Mihaila, ITP Heidelberg37. Dominique Mouhanna, Université Pierre et Marie Curie38. Sandor Nagy, University of Debrecen39. Yuichi Ohara, Nagoya University40. Jordi París-López, University of Graz41. Carlo Pagani, University of Mainz42. Jan Pawlowski, ITP Heidelberg43. Roberto Percacci, SISSA, Trieste44. Hans-Jürgen Pirner, ITP Heidelberg45. Alessia Platania, INAF, Catania46. Martin Pospiech, University of Darmstadt47. Srinivas Raghu, Stanford University48. Manuel Reichert, ITP Heidelberg49. Fabian Rennecke, ITP Heidelberg50. Martin Reuter, Mainz University51. Dirk Rischke, University of Frankfurt52. Manfred Salmhofer, ITP Heidelberg53. Ippocratis Saltas, IASS54. Francesco Sannino, CP3-Origins, Odense55. Frank Saueressig, Radboud University, Nijmegen56. Michael Scherer, ITP Heidelberg

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57. Michael Schmidt, ITP Heidelberg58. Giulio Schober, ITP Heidelberg59. Julien Serreau, APC, Université Paris Diderot60. Misha Shaposhnikov, EPFL, Lausanne61. Davide Squizzato, LPMMC, Université Grenoble Alpes62. Imola Steib, University of Debrecen63. Dennis Stock, ITP Heidelberg64. Malo Tarpin, LPMMC, Université Grenoble Alpes65. Nikos Tetradis, University of Athens66. Ronny Thomale, Würzburg University67. Eduard Thommes, ITP Heidelberg68. Matthieu Tissier, Université Pierre et Marie Curie69. Gian Paolo Vacca, INFN70. Fleur Versteegen, ITP Heidelberg71. Christof Wetterich, ITP Heidelberg72. Sebastian Wetzel, ITP Heidelberg73. Nicolas Wink, ITP Heidelberg74. Masatoshi Yamada, ITP Heidelberg

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