Gauge/Gravity Duality and Particle Physics: New approaches...
Transcript of Gauge/Gravity Duality and Particle Physics: New approaches...
.
Gauge/Gravity Duality and Particle Physics:
New approaches to strongly coupled sectors
Johanna Erdmenger
Julius-Maximilians-Universitat Wurzburg
1
Motivation and Outline
Gauge/Gravity Duality
New development in quantum field theory and string theory
Generalizes the AdS/CFT correspondence
Maps strongly coupled gauge theories to weakly coupled gravity theories
Intrinsic fundamental interest for gravity
Applications: Low-energy QCD
Applications: Composite Higgs
2
Motivation
Applications also in nuclear and condensed matter physics
Example: Strongly coupled hot and dense medium / quark-gluon plasma
AdS/CFT prediction for ratio shear viscosity/entropy density agrees withmeasurements at RHIC, LHC
η
s=
1
4π
~kB
Kovtun, Son, Starinets 2004
3
Motivation
Gauge/Gravity Duality for particle physics:
Non-supersymmetric, confining gauge theories are obtained by deformingthe original AdS/CFT correspondence with relevant operators
Embedding in string theory guarantees control of parameters
UV completeness
Duality allows to calculate masses and decay constantsin strongly coupled theories with spontaneous chiral symmetry breaking
4
Applications within particle physics
QCD at low energies: Chiral symmetry breaking and confinement
Applications within particle physics
QCD at low energies: Chiral symmetry breaking and confinement
Composite Higgs: The Higgs particle as a pseudo-Goldstone boson
Applications within particle physics
QCD at low energies: Chiral symmetry breaking and confinement
Composite Higgs: The Higgs particle as a pseudo-Goldstone boson
Deep inelastic scattering at very small x: Uncover universal behaviour
5
Composite Higgs
Dynamical electroweak symmetry breaking (Weinberg 1976)
Higgs as pseudo-Goldstone boson of global symmetry (Kaplan, Georgi 1984)
SSB of global SU(4) symmetry (phenomenologically viable)(Agashe, Contino, Pomarol; Cacciapaglia, Ferretti; Gherghetta ....)
mixing between top quark and composite fermions
slow running of couplings
Composite Higgs
Dynamical electroweak symmetry breaking (Weinberg 1976)
Higgs as pseudo-Goldstone boson of global symmetry (Kaplan, Georgi 1984)
SSB of global SU(4) symmetry (phenomenologically viable)(Agashe, Contino, Pomarol; Cacciapaglia, Ferretti; Gherghetta ....)
mixing between top quark and composite fermions
slow running of couplings
Gauge/gravity duality:Calculation of masses and decay constantsfor strongly coupled theories with SSB
Gauge/gravity duality models constrained by string theory(Different from Randall-Sundrum models)
6
Gauge/Gravity Duality
Duality:
Gauge/Gravity Duality
Duality:
Gauge/Gravity Duality:
A theory without gravity is dual to a gravity theory.
7
Gauge/gravity duality
Gauge/gravity duality
Conjecture which follows from a low-energy limit of string theory
Duality:
Quantum field theory at strong coupling⇔ Theory of gravitation at weak coupling
Holography:
Quantum field theory in four dimensions⇔ Gravitational theory in five dimensions
8
Foundations: Gauge/gravity duality
Best understood example: AdS/CFT correspondence
AdS: Anti-de Sitter space, CFT: Conformal field theory
9
Anti-de Sitter Space
Space of constant negative curvature, has a boundaryds2 = e2r/Ldxµdx
µ + dr2Figure source: Institute of Physics, Copyright: C. Escher
10
Conformal field theory
Quantum field theory
in which the fields transform covariantly under conformal transformations
Conformal coordinate transformations:
Preserve angles locally: dx′µdx′µ = Ω2(x)dxµdxµ
Correlation functions are determined up to a small number of parametersJ.E., Osborn ’97
In AdS/CFT correspondence: Conformal field theory in 3+1 dimensions:N = 4 SU(N) Super Yang-Mills theory (global symmetry SO(4, 2)× SU(4))
11
AdS/CFT correspondence
‘Dictionary’ Gauge invariant field theory operators⇔ Classical fields in gravity theory
Symmetry properties coincide
Test: (e.g.) Calculation of correlation functions
12
AdS/CFT correspondence
Field-operator correspondence:
〈e∫ddxφ0(~x)O(~x)〉CFT = Zsugra
∣∣∣φ(0,~x)=φ0(~x)
Generating functional for correlation functions of particular composite operatorsin the quantum field theory
coincides with
Classical tree diagram generating functional in supergravity
13
AdS/CFT correspondence
String theory origin⇒ Ten dimensions
AdS5 × S5
Symmetries of field theory and geometry coincide: SO(4, 2)× SO(6)
Internal manifold determines field content
14
String theory origin of the AdS/CFT correspondence
near-horizon geometryAdS x S
55
D3 branes in 10d
duality
⇓ Low energy limit
Supersymmetric SU(N) gau-ge theory in four dimensions(N →∞)
Supergravity on the spaceAdS5 × S5
15
AdS/CFT correspondence
16
Book on gauge/gravity duality
17
Generalized AdS/CFT Correspondence: Gauge/Gravity Duality
Generalization of AdS/CFT to quantum field theories of experimental relevance?
Generalized AdS/CFT Correspondence: Gauge/Gravity Duality
Generalization of AdS/CFT to quantum field theories of experimental relevance?
Prototype candidate: Low-energy QCD
Generalized AdS/CFT Correspondence: Gauge/Gravity Duality
Generalization of AdS/CFT to quantum field theories of experimental relevance?
Prototype candidate: Low-energy QCD
SU(3) gauge theory with matter (gluons and quarks)
Strongly coupled at low energies⇒ mesons, baryons
Beta function negative
Generalized AdS/CFT Correspondence: Gauge/Gravity Duality
Generalization of AdS/CFT to quantum field theories of experimental relevance?
Prototype candidate: Low-energy QCD
SU(3) gauge theory with matter (gluons and quarks)
Strongly coupled at low energies⇒ mesons, baryons
Beta function negative
Relax symmetry requirements of original AdS/CFT in controlled way
Add quark degrees of freedom Additional D-brane probes
18
Chiral symmetry breaking within generalized AdS/CFT
Combine the deformation of the supergravity metricwith the addition of brane probes:
Dual gravity description of chiral symmetry breaking and Goldstone bosons
J. Babington, J. E., N. Evans, Z. Guralnik and I. Kirsch,
“Chiral symmetry breaking and pions in non-SUSY gauge/gravity duals”
Phys. Rev. D 69 (2004) 066007 [arXiv:hep-th/0306018].
19
Applications to QCD-like theories: Light mesons
Babington, J.E., Evans, Guralnik, Kirsch PRD 2004
Gravitational realization of
Spontaneous chiral symmetry breaking
New ground state given by quark condensate 〈ψψ〉
Spontaneous symmetry breaking→ Goldstone bosons (Mesons)
20
Light mesons
Babington, J.E., Evans, Guralnik, Kirsch PRD 2004
Add D7-Branes (eight-dimensional surfaces) to ten-dimensional space
π pseudoscalar meson mass: From fluctuations of D-brane
ρ vector meson mass: From fluctuations of gauge field on D-brane
21
Comparison to lattice gauge theory
Mass of ρ meson as function of π meson mass2 (for N →∞)
0 0.25 0.5 0.75 1
(mπ / mρ0)2
1
1.2
1.4
mρ /
mρ0
Lattice extrapolationAdS/CFT computationN= 3N= 4N= 5N= 6N= 7N=17
22
Comparison to lattice gauge theory
Gauge/Gravity Duality: J.E., Evans, Kirsch, Threlfall ’07, review EPJA
Lattice gauge theory: Lucini, Del Debbio, Bali, Panero et al ’13
Result Gauge/Gravity Duality:
mρ(mπ)
mρ(0)= 1 + 0.307
(mπ
mρ(0)
)2
Result Lattice Gauge Theory (Bali, Bursa ’08): Slope 0.341± 0.023
23
Gauge/gravity dual model for composite Higgs
J.E., Evans, Porod
Toy model: Composite Higgs similar to η′ of QCD
Introduce fermions into gravity action
Given by Dirac-Born-Infeld action of string theory
SfD7
=TD7
2
∫d8ξ√− det gAB ΨP−Γ
A(DA +
1
2× 8× 5!FNPQRSΓ
NPQRS(iσ2) ΓA
)Ψ
Abt, J.E., Evans, Rigatos to appear
Gauge/gravity dual model for composite Higgs
J.E., Evans, Porod
Toy model: Composite Higgs similar to η′ of QCD
Introduce fermions into gravity action
Given by Dirac-Born-Infeld action of string theory
SfD7
=TD7
2
∫d8ξ√− det gAB ΨP−Γ
A(DA +
1
2× 8× 5!FNPQRSΓ
NPQRS(iσ2) ΓA
)Ψ
Abt, J.E., Evans, Rigatos to appear
Programme:Calculate composite Higgs and fermion masses, decay constants
Include SU(4) global symmetry
24
Conclusions and outlook
Gauge/gravity duality :
Duality between quantum field theories and gravity
New approach for describing strongly coupled gauge theories
mapped to classical gravity theories
Calculation of bound state masses and decay constants
Application examples within particle physics:
– QCD– Composite Higgs models
25