anomalies and transport - univie.ac.at · anomalies -> parity violating transport magnetic...

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. 107 (2011) 021601)

arXiv:1107.0368 (JHEP 1109 (2011) 121 )

8th Central European Seminar on Particle Physics and QFT, Vienna, 20111Tuesday, November 22, 2011

OutlineThe Chiral Magnetic Effect

Kubo formulas I

Kubo formulas II

Hydrodynamics

Strong coupling (Holography)

Observable gravitational anomaly?

Summary

[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]

2Tuesday, November 22, 2011

The Chiral Magnetic Effect

B+

-

[Kharzeev, McLarren, Warringa]

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

-



B+

-

Magnetic Field



-



B+

-

Net chirality

Magnetic Field



-



B+

-

Electric current

J i =µ5

2π2Bi

Net chirality

Magnetic Field



-



B+

-

Electric current

J i =µ5

2π2Bi

Net chirality

Magnetic Field

P-odd charge separation



-


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]5Tuesday, November 22, 2011

Kubo formulas I chiral fermions

chemical potentials and Cartan generators

1-loop calculationAnomalycoeff

[Newman, Son], [Newman]5Tuesday, November 22, 2011

Kubo formulas I

∼ dABC

TA

TB TC

AμA pure gauge

AνB AρC


Kubo formulas IIfinite density: charge transport => energy transport

energy flux sourced by magnetic fields

at ω=0 reverse order of operators


Kubo formulas IIfinite density: charge transport => energy transport

energy flux sourced by magnetic fields

at ω=0 reverse order of operators

conductivity ?7Tuesday, November 22, 2011

Tμν sourced by metric

Ag “gravitomagnetic field” -> chiral gravitomagnetic effect

chiral vortical effect: fluid velocities

Kubo formulas II


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


Anomalies


Jµ = nuµ + σPµν∂ν� µ

T

�uλ + νµ

Hydrodynamicsalso energy flux

hydrodynamics:

[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

Tµν = (�+ P )uµuν + Pgµν + ησµν + ζPµν∂λuλ +Qµuν +Qνuµ


anomalous contributions

Jµ = nuµ + σPµν∂ν� µ

T

�uλ + νµ

Hydrodynamicsalso energy flux

hydrodynamics:

[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

Tµν = (�+ P )uµuν + Pgµν + ησµν + ζPµν∂λuλ +Qµuν +Qνuµ


νµA = σBABBB,µ + σV

Aωµ

Qµ = ρBABA,µ + ρVAωµ

BA,µ =1

2�µνρλuνFA

ρλ

ωµ = �µνρλuν∂ρuλ

σBAB =

1

4π2dABCµ

C

σVA = ρBA =

1

8π2dABCµ

BµC +T 2

24bA

ρV =1

12π2dABCµ

AµBµC +T 2

12bAµ

A

Hydrodynamics


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 !

�JJ� = −ipz� κ

2πGµ− κ

6πGβ�


T 0i =µ5

6T 2ωi

J i5 =

�µ2 + µ2

5

4π2+

T 2

6

�ωi

Observe grav. Anomaly?

[Karen-Zur, Oz]

ωi

Enhanced Ω_ Production

Better Observable? Energy!

Eup > Edown

measurable effect?


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 gravitational CS term

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

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


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