Effective field theory, holography, and non-equilibrium ...
Transcript of Effective field theory, holography, and non-equilibrium ...
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<Tc
Gubser,Hartnoll,Herzog,Horowitz
Bulkchargeactslikeascreen,preventingchargedexcitationsfromfallingintothehorizonanddissipating:itisasuperfluid.
Superfluidcomponent:bulkcharge;normal:blackholegeometry
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