Anomalies and Transport

Karl LandsteinerInstituto de Física Teórica, UAM-CSIC

in collaboration withI. Amado, E. Megías, L. Melgar, F. Peña-Benitez,

arXiv:1102.4577 (JHEP 1105.5006)arXiv:1103.5006 (Phys. Rev. Lett.)

to appear

11th Workshop on non-perturbative QCD Paris 2011

OutlineMovie

The CME (flash review)

Kubo formulas I

Hydrodynamics

Kubo formulas II

weak coupling

strong coupling

[Kharzeev, McLarren, Warringa, Nucl. Phys A803,227, arXiv:0706.1026][Fukushima, Kharzeev, Warringa, Phys. Rev. D78, 074033, arXiv:0706.1026][Kharzeev, Warringa, Phys. Rev. D80 (2009) 034028, arXiv:0907.5007]

RHIC’s hot quark soup

Please click below for an introductory movie

http://youtu.be/kXy5EvYu3fw

The CME

B

J

+

-

Text

[Kharzeev, McLarren, Warringa]

[Ruggieri’s talk]

[parity violating currents: Vilenkin ’80, Giovannini, Shaposhnikov ’98, Alekseev, Chaianov, Frohlich ’98]

The CME

B

J

+

-

Magnetic Field

Text

[Kharzeev, McLarren, Warringa]

[Ruggieri’s talk]

[parity violating currents: Vilenkin ’80, Giovannini, Shaposhnikov ’98, Alekseev, Chaianov, Frohlich ’98]

The CME

B

J

+

-

Net chirality

Magnetic Field

Text

[Kharzeev, McLarren, Warringa]

[Ruggieri’s talk]

[parity violating currents: Vilenkin ’80, Giovannini, Shaposhnikov ’98, Alekseev, Chaianov, Frohlich ’98]

The CME

B

J

+

-Electric current

Net chirality

Magnetic Field

Text

[Kharzeev, McLarren, Warringa]

[Ruggieri’s talk]

[parity violating currents: Vilenkin ’80, Giovannini, Shaposhnikov ’98, Alekseev, Chaianov, Frohlich ’98]

The CME

B

J

+

-Electric current

Net chirality

Magnetic Field

P-odd charge separation

Text

[Kharzeev, McLarren, Warringa]

[Ruggieri’s talk]

[parity violating currents: Vilenkin ’80, Giovannini, Shaposhnikov ’98, Alekseev, Chaianov, Frohlich ’98]

Kubo formulas IChiral magnetic conductivity

Kubo formula, general symmetry group

[Kharzeev, Warringa]�J = σ �B

σAB = limpj→0

�

i,k

i

2pj�ijk�JA

i JBk �

����ω=0

Kubo formulas I chiral fermions

chemical potentials and Cartan generators

1-loop calculation

[Newman, Son], [Newman]

Kubo formulas I chiral fermions

chemical potentials and Cartan generators

1-loop calculationAnomalycoeff

[Newman, Son], [Newman]

Kubo formulas I

∼ dABC

TA

TB TC

AμA pure gauge

AνB AρC

Kubofinite density: charge transport => energy transport

energy flux sourced by magnetic fields

at ω=0 reverse order of operators

[Neiman, Oz], [Loganayagam], [Kharzeev, Yee]

Kubofinite density: charge transport => energy transport

energy flux sourced by magnetic fields

at ω=0 reverse order of operators

conductivity ?

[Neiman, Oz], [Loganayagam], [Kharzeev, Yee]

KuboTμν sourced by metric

Ag “gravitomagnetic field” -> chiral gravitomagnetic effect

chiral vortical effect: fluid velocities

Hydrodynamicsalso energy flux

hydrodynamics:

Landau frame:

[Son,Surowka], [Eling, Neiman, Oz], [Erdmenger, Haack, Kaminski, Yarom], [Banerjee, Bhattacharya, Bahattacharya, Dutta Loganayagam, Surowka], [Loganayagam] [Kharzeev, Yee] [Sadovyev, Isachenkov, Zakharov]

limpj→0

i

2pj

�

i,k

�ijk �T0iT0k�|ω=0 �= 0

Hydrodynamicsξ coefficients are different from σ’s

hydro in alternative frame:include “heat currents”

kubo formulas IIas before: general symmetry group

kubo formulas IIas before: general symmetry group

Integration constantgravitational anomaly!

Kubo formulas II

∼ tr (TA)TA

gμν gλρ

AμA pure gauge

Kubo formulas II

Anomaly

axial current of one Dirac fermion

[Vilenkin ’80]

Holographymixed gauge gravitational Chern Simons term

current

on-shell we recover the anomaly

[H.U. Yee], [Gynther, KL,Pena-Benitez, Rebhan] [Kalayhdzian, Kirsch], [Gorski, Zayakin]

HolographyKubo formulas: fluctuations

background: charged AdS black hole

correlators are

coeffs consistent with weak coupling

no T^3 terms !

[Neiman, Oz], [Loganayagam]

�JJ� = −ipz� κ

2πGµ− κ

6πGβ�

SummaryAnomalies -> parity violating transport

Magnetic fields or vortices

We have derived Kubo formulas

(non)-renormalizaton

Surprise: mixed gauge gravitational anomaly contributes

Hydrodynamics and derivative expansion? (fluid/gravity)

Holography with gravitaitonal CS term

Observable effects? [Karen-Zur, Oz], [Kharzeev, Son], [Kharzeev, Yee]

SummaryAnomalies -> parity violating transport

Magnetic fields or vortices

We have derived Kubo formulas

(non)-renormalizaton

Surprise: mixed gauge gravitational anomaly contributes

Hydrodynamics and derivative expansion? (fluid/gravity)

Holography with gravitaitonal CS term

Observable effects? [Karen-Zur, Oz], [Kharzeev, Son], [Kharzeev, Yee]