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
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