Chiral Transport and theHydrodynamic Frames

Navid AbbasiIPM(Tehran)

Basedonworks:[1508.068791509.088781612.0864170?.????]

IncollaborationwithA.Davody,K.Hejazi,Z.Rezaei,D,Allahbakhshi,F.Thaghavi,F.Taghinavaz,K.Naderi

0. Outline• Relativistic hydro• Motivation for hydrodynamic chiral transport• Non-dissipative featureof chiral transport• Spectrumof chiral hydromodes• Chiral hydromodes fromKinetic theory• Frame choice and hydromodes

1. Hydrodynamics

Responseofthesystemtoperturbations:atlowenergy andLongwave-length limit

Equationsofhydroarelocalconservationequationsvariables

Mainideaofhydro:14 variablesintermsof5 variables

2. Dual gravity picture?Early studies:

MembraneParadigm:Fluidonthehorizon[Damur;ThornePriceMacdonald1970’s]

New viewpoint:Fluid-Gravity Duality:Fluidontheboundary

[BhattacharyyaHubenyMinwalla Rangamani 2007]

3. Extensions of Fluid-Gravity:

1. ForcedFluid[BhattacharyyaLoganayagamMinwalla Nampuri Trividi 2007]

2. Non-RelativisticFluid[BhattacharyyaMinwalla Wadia 2008]

3. (Chirally)ChargedFluid[Erdmenger Haack KaminskiYarom 2008]

[BanerjeeBhattacharyyaBhattacharyyaDuttaLoganayagamSurowka 2008]

anomaly

vorticity:

5. Hydro with triangle anomalies:

Motivated by Fluid/Gravity:In the presenceof anomalies onemay add parity odd terms:

In Landau-Lifhitz frame[SonSurowka 2009]

[Kharzeev Yee;NeimanOz2011]

[JensenLoganayagam Yarom 2012]

6. Chiral transport is non-dissipative:OhmLaw: dissipative

(-)(-)(+)

London2nd eq.: non-dissipative(+)(+)(+)

Transportinsystemofnon-dissipativeSingleright-handedfermions: (-) (+)(-)

7. A more realistic model :

Chiralhydrodynamics withbothvectorandaxialcurrents:

with

[GaoLiangPuWangWang2012]

[LandsteinerMegias Pena-Benitez2013]

8. Hydro excitations in a chiral system:

Long-wavelengthexcitationsaroundequilibrium:

perturbingthehydrofields:

9. Fluid coupled to weak magnetic field

6 linearcoupledequationsgive6 hydromodes:

1,2:Chiral-Magnetic-Heat wave:3,4:Ordinarysoundwave:5,6:ChiralAlfven wave:

10. Chiral –Magnetic-HeatWave

[N.AAllahbakhshi Davody Taghavi 2016]

Equationofstate

11. CMHW in QGP:It iswell-understood that the QGP produced in HIC in initially non-chiral:

CMW:[Kharzeev,Yee.2012]

12. Rotating Fluid coupled to weak magneticfieldScalarsector:mixedchiral-magnetic-vortical-heatwave

bluecurve:

13. Out of equilibrium dynamics from KinetictheoryChiralparticlesinkinetictheory:ChiralKineticTheory

[Stephanov Yee 2012][SonYamamoto2012]

Berry Curvature Berry Flux

Kineticequation:

14. Conservation equations in CKT:distributionfunction

Integratingthekineticequationsaftermultiplyingwithcollisioninvariantquantities:Collisioninvariant.ConservationEq.CorrespondingHydroEq.

15. Hydro modes from CKT

Forslowly-varyingmacroscopicfields,weexpandthedistributionfunctionaroundthethermodistribution:

tofindthelinearizedequations:

with:

16. Comparison between Hydro in LL and CKT

Forafluidofsingleright-handedfermionsat..:kinetictheoryrelativistichydro

17. Hydrodynamic frames:Beyondthezeroorderinderivativeexpansion,thereisanambiguity indefininghydrovariables.Onecanmaketransformations

[BhattacharyaBhattacharyya

Minwalla Yarom 2011]

whilephysicalquantities,andremaininginvariant.

Constructedbyindependentone-derivativedata

Eachchoiceofframeisequivalenttoonewayoffixingthisambiguity.

18. In the absence of dissipation

ThermodynamicframeLandau-Lifshitz

[Landsteiner.2017]

19. Hydrodynamic modes are not frameinvariant

Thermodynamic(Lab) Landau-Lifshitz.Boost

Physicalframe,consistentwithVilenkin 89 results.“No-dragframe:[Stephanov Yee2015]”

20. QCD fluid:Insinglechiralityfluid: CAWdoesnotexist.[Yamamoto2105]

[N.ADavody Rezaei Hejazi 2016]

InQCDtypefluid:CAWdoesexist:

Gauge-gravitationalanomalyinQGP.

21. Open questions

1.Howwouldchangethesituationwhenthemagneticfieldisdynamical?

2.WillbetheCAWpropagatewhenconsideringtheback-reactioneffects?

3.Thefullspectrumofchiralmagnetohydrodynamics?

Thankyou