Effectivefieldtheory,holography,andnon-equilibriumphysics

HongLiu

Equilibriumsystems

Forequilibriumsystems:

Renormalizationgroup,universality

Microscopicdescription

Macroscopicphenomena

lowenergyeffectivefieldtheory:

Directcomputation:almostalwaysimpossible

Ginsburg-Landau-Wilsonparadigm

Expressfreeenergyintermsofappropriatelowenergyd.o.f.,constrainedonlybysymmetries

Couldinprinciplebegeneralizedtonon-equilibriumsystems,but….

Non-equilibriumsystemsMicroscopicdescription

Macroscopicphenomena

Manytheoreticalapproaches,

“Too”microscopic:likeLiouvilleequation,BGKKYhierarchy,Boltzmannequation…...

“Too”phenomenological:hydrodynamics,stochasticsystems…

Inthistalk:twonewapproaches

1.non-equilibriumeffectivefieldtheory

2.Holographicduality

(toomanyd.o.f ortooformal)

Firstprinciple,withsmallnumberofd.o.f.

Non-equilibriumeffectivefieldtheory

PathintegralinageneralstateNon-equilibriumproblems:interestedindescribingnonlineardynamicsaroundastate.

Shouldbecontrastedwithpathintegralfortransitionamplitudes,

Closedtimepath(CTP)orSchwinger-Keldysh contour

Non-equilibriumeffectivefieldtheoryMicroscopicSchwinger-Keldysh pathintegral:(double#ofd.o.f.)

Integrateoutall“massive”modes:

1.Whatare?

notmanageablebeyondperturbationtheory

2.Whatarethesymmetriesof?

Dependonclassofphysicalsystemsand

Lowenergygaplessmodes(twosets)

Non-equilibriumEFT

Renormalizationgroup,universality

Microscopicdescription

Macroscopicphenomena

lowenergyeffectivefieldtheory:

Notmuchexplored

Example:effectivefieldtheoryforgeneraldissipativefluids.

Effectivefieldtheoryfordissipativefluids

PaoloGloriosoMichaelCrossley

arXiv:1511.03646

SeealsoHaehl,Loganayagam,RangamaniarXiv:1510.02494,1511.07809

FluiddynamicsConsideralong wavelengthdisturbanceofasysteminthermalequilibrium

conserved quantities:cannot relaxlocally,onlyviatransportsGaplessandlong-livedmodes(universal)

non-conserved quantities:relaxlocally,

Hydrodynamics

dynamicalvariables:(localequilibrium)slowlyvaryingfunctionsofspacetime

Phenomenologicaldescription:

O’Haraetal(2002)

Despitethelongandglorioushistoryofhydrodynamics

Itislikeameanfieldtheory,doesnotcapturefluctuations.

Therearealwaysstatistical fluctuations…..

transports,

Importantinmanycontexts:

Atlowtemperatures,quantum fluctuationscanalsobeimportant.

Longtimetail,

dynamicalaspectsofphasetransitions,

non-equilibriumstates,

turbulence,

finitesizesystems….

Phenomenologicallevel:stochastic hydro(Landau,Lifshitz)

:noiseswithlocalGaussiandistribution,fluctuation-dissipationrelations

3.fluctuationsofdynamicalvariablesthemselves

Far-from-equilibrium:

1.interactionsamongnoises

2.interactionsbetweendynamicalvariablesandnoises

Untilnownosystematicmethodstotreatsuchnonlineareffects.

non-equilibriumfluctuation-dissipationrelations?

Goodfornear-equilibriumdisturbances

Searchingforanactionprinciplefordissipativehydrodynamicshasbeenalongstandingproblem,datingback atleasttotheidealfluidactionofG.Herglotz in1911.

Manyactivitiessince70’stounderstand hydrodynamicfluctuations,longtimetails…

SearchingforanEFTdescriptionshouldbedistinguishedfromsearchinganactionwhichjustreproducesconstitutiverelations(whichmaynotcapturefluctuationscorrectly).

Wewillbeabletoaddresstheseissuesbydevelopinghydrodynamicsasanon-equilibriumeffectivefieldtheoryofageneralmany-bodysystematafinitetemperature.

Subsequent work include Taub, Salmon; Jackiw et al.; Andersson et al.

The last decade has seen a renewed interest: including, Dubovsky,Gregoire,Nicolis andRattazzi inhep-th/0512260andfurtherdeveloped byDubovsky,Hui,Nicolis andSon,Grozdanov et al, Haehl et al, Kovtun et al ….

Holographic derivation: Nickel, Son; de Boer, Heller, Pinzani-Fokeeva; Crossley, Glorioso., HL, Wang.

Hydroeffectivefieldtheory

hydrodynamicmodes(2sets)

1.Whatare? donotwork

2.Whatarethesymmetriesof?

3.Integrationmeasure?

Atlongdistancesandlargetimes:

Allcorrelationfunctionsofthestresstensorandconservedcurrentsinthermaldensitymatrix

DynamicalvariablesRecallLagrangedescriptionofhydrodynamics:

:labelfluidelements : describefluidmotion

Forageneralmany-bodysysteminagenericdensitymatrixstate,wedevelopedan”integrating-in”proceduretoshowthat gaplessd.o.f.associatedwithaconservedstresstensor canbedescribedby:

:internaltime

Standardhydrovariables(whicharenowderivedquantities)

Noise:

Asignificantchallenge:ensuretheeoms fromtheactionofXcanbesolelyexpressedintermsofthesevelocity.(e.g.solids v.s.fluids)

Symmetries

Requiretheactiontobeinvariantunder:

labelindividualfluidelements, internaltime

definewhatisafluid!

Itturnsoutthesesymmetriesindeeddomagicforyou:

atthelevelofequationsofmotion,theyensurealldependenceondynamicalvariablescanbeexpressedinandtemperature.

Recoverstandardformulationofhydrodynamics(modulo phenomenological constraints)

ConsistencyconditionsandsymmetriesWeareconsideringEFTforasystemdefinedwithCTP:

Whencoupledtoexternalsources:

• Reflectivitycondition:

• Unitarity condition:

RequirestheactiontosatisfyaZ2 reflectionsymmetry

Introducefermionic partnerseachfordynamicalvariablesandrequiretheactiontohaveaBRSTtypesymmetry.

complexaction,fluctuationsofnoisesaredamped.

• KMSconditionplusPTimplyaZ2 symmetryonW:

LocalKMScondition:Z2symmetry

Non-equilibriumfluctuation-dissipationrelations

AlltheconstraintsfromentropycurrentconditionandlinearOnsagerrelations

NewconstraintsonequationsofmotionfromnonlinearOnsagerrelations.

supersymmetry

Summary1.Hydrodynamicswithclassicalstatisticalfluctuations

isdescribedbyasupersymmetric quantum fieldtheory

2.Hydrodynamicswithquantumfluctuationsalsoincorporated

isdescribedbya“quantum-deformed”(supersymmetric)quantumfieldtheory.

Example:nonlinearstochasticdiffusion

Considerthetheoryforasingleconservedcurrent,wheretherelevantphysicsisdiffusion.

Dynamicalvariables: (or)

Roughly,:standarddiffusionmode,:thenoise.

Ifignoringinteractionsofnoise

AvariationofKardar-Parisi-Zhang equation

Applications

transports,

Longtimetail,

dynamicalaspectsofphasetransitions,

non-equilibriumstates,

turbulence

…...........

Holographicdualityand

non-equilibriumsystems

HolographicdualityMaldacena; Gubser, Klebanov,Polyakov;Witten

Extradimension:geometrization ofrenormalizationgroupflow!

shortdistance(UV)

longdistance(IR)

Aprototypeexample

N =4Super-Yang-Millstheoryin(3+1)dimensionswithgaugegroupSU(N)

Maldacena (1997)

Astringtheoryin5-dimensionalanti-deSitter spacetime

anti-deSitter(AdS):homogeneousspacetimewithnegativecosmologicalconstant.

scaleinvariantArelativeofQCD

Classicalgravitylimit(Einsteingravityplusmatterfields)

StronglycoupledandlargeN limit

=

=Manyexamplesindifferentspacetime dimensions known.

Previously impossibleproblems instronglycoupled systemscannowbemappedtosolvable problemsclassicalgravity!

Anti-deSitter(AdS)spacetime

t

Boundary

AdS spacetime isalikeafinitesizebox,confinedbygravitationalpotential

Dictionary

BulkBoundarystates states/geometries

operators fields

• Spin, charge • Spin, charge• dimension • mass

• metric

• Gaugefield

Partitionfunction Partitionfunction

Correlationfunctions Scatteringamplitudes

…..... ….....

•

•

ThermalstateThermalstate Schwarzschild

blackhole

Macroscopicbehaviordictatedbyblackholegeometry

Finitechargedensitystate

Chargedblackhole

Powerofholographicdualitystrongcouplinglimit Classicalgravity

1. Greatlyreducesthenumberofdegreesoffreedom

Quantummany-body classicalfew-body

Cantrackrealtimeevolution

2.highlyquantummechanical,strongcouplingphenomenaoftenfollowsfromsimplegeometricpictureorgravitationaldynamics

3.Geometrization ofRG:likeamagnifyingglasshelpingunderstandphysicsateveryscale

Microscopicdescription

Infrared?

Boundary

zIRgeometry

IRfixedpointGapped

Finitetemperature

IRscalinggeometryIRgeometryendsatfiniteproperdistance

Blackholehorizon

IRphysics

Holographyandnon-equilibriumphysics

Holographicdualityalreadyledtomanynewinsightsintonon-equilibriumphysics

Near-equilibrium: transports

Farfrom-equilibrium: Quantumturbulence

Manyothertopics:

Relaxation:quasi-normalmodes

Quantumquenches

Thermalization:unreasonableeffectivenessofhydro….......

Non-equilibriumsteadystates

Dissipation

Shearviscosityfromgravity

BHσ :absorptioncrosssectionofgravitons byablackhole.

Fieldtheory:slightlydeformthemetricofspacetime.

Gravitypicture:

Kovtun,Policastro,Son,Starinets

Transports

DCelectricconductivity,thermalconductivitiesandbulkviscosityallcapturedbygeometriesatthehorizon.

DCconductivity Blake,TongGauntlett,Donos,…....“anti-Matthiessen's rule”

QuantumTurbulenceIrregular,chaoticmotionofsuperfluidvortices

Feynman1955Viven,1957

Mauer andTabeling,1997

e.g.Kolomogorov scaling

Someoutstandingquestions:

DoestheobservedKolomogorov scalinghasaclassicalorigin?

anenergycascadeanddirectionofthecascade?Especially2+1d

Dissipationmechanism?

“Quasi-classical”quantumturbulenceSmith,Donnelly,Goldenfeld,Viven,1993……….

Holographicduality(firstprinciplecalculation)canprovidedefiniteanswerstothesequestions Chesler,HL,Adams,Science341,368(2013)

HolographicSuperfluid

Holographyrelatesasuperfluidin2+1dimensionstoclassicalelectrodynamics +chargescalar+gravity in3+1dimensions.

boundary

horizon

Charge and scalar condensateT

Vortices in the superfluid (blue disks on top) extend to flux tubes --- holes in the screen.

Holographicsuperfluidwithvortices

2+1dimensionalboundary

Energycanfallthroughtheseholesintotheblackhole.Vorticesthusallowdissipation.

InitialconditionsInitial data: periodic lattice of winding number n = ±6 vortices.

We consider T ⇡ 0.6Tc Tc ⇡ 0.06µ

Superfluid can dissipate into the normal component, but the effects on the normal component are neglected. (works for T not too low)

Superfluid: 77% Normal: 23%

KineticEnergySpectrumScalingwithkChesler, HL, Adams

k�53 k�3

Scalingrange: Averagevortexspacing

Indicatesquantumeffectssignificant!

Energy can fall through these holes into the black hole.

Dissipationscale:

kdiss =2�

vortex size

Vortices: holes in the screen

Vortex size ⇡ 1 kdiss ⇡ 2� > �+ ⇡ 3

Direct energy cascade ! confirmedbydirectdriving

SummaryKolomogorov scaling

Energydissipationthroughvortexannihilationsbyleakingthroughvortexcore

Directcascadein(2+1)-dimensionincontrasttotheinversecascadeofordinaryfluidturbulence

Mustbeofquantumorigin

ThankYou