lecture25 ads black holes and thermal gauge theory polyakov-susskind loop, screening, quasinormal modes, hawking-page transition

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1、MITOpenCourseWarehttp://ocw.mit.edu8.821StringTheoryFall2008ForinformationaboutcitingthesematerialsorourTermsofUse,visit:http://ocw.mit.edu/terms.8.821F2008Lecture25:ThermalaspectsofN=4SYMLecturer:McGreevy12/10/081TheN=4plasmaatlargeλPreviouslyinlect

2、ure23wegaveevidencethattheBlackHolethermodynamicsoftheAdSBlackBrane(non-extremal)solutionwasdualtothethermalensembleofN=4SYMonR3atlargeNandλ.ThusthegaugetheoryprovidesthemicrostatesthatarebeingcoarsegrainedbytheBekenstein-Hawkingentropyoftheblackhole

3、SBH.Afewcommentsonthisobservation:1.1Hydrodynamics•Perturbingtheequilibriumoftheboundarytheorywithakickwillresultinthermalizationrelaxationbacktoequilibrium.•Inthebulktheresponsetosuchakickisfortheenergyofthekicktofallintotheblackhole.Theabovetwostat

4、ementsarerelatedbytheduality.InthelongwavelengthandsmallfrequencylimitbothareconsistentwiththehydrodynamicsofarelativisticCFT.Additionallythedualityallowsonetocomputevarioustransportcoefficientsofthegaugetheoryatlargeλ,suchastheshearviscosity,R-chargec

5、onductivity,etc.Seethereview[1].1.2ThermalScreeningAtfinitetemperatureTcorrelatorsdieoffexponentiallyatlargeseparationr≫1/T,evenifinvacuumtherearemasslessfieldswhichmediatelongrangeinteractions.Thisisbecausesuchparticlesdevelopathermalmassfromcontinuous

6、lyinteractingwiththethermalbath.Forexampletheforcebetweentwoexternalchargesinagaugetheoryshouldbehaveatlargedistancesas,V(r)∼e−mthr(1)qq¯r≫1/T1TTTTFigure1:Aparticlereceivesmultiplekicksfromitsthermalsurroundings.Thisgeneratesathermalcontributiontothe

7、particlesmass.wheremthisthethermalmass.Theqq¯potentialcanbecalculatedusingaWilsonloop,�������exp−iVqq¯(r)T˜=PexpiA≡�WCr�T(2)CrTwherethecontourCrisarectanglewithspatialseparationrandtemporalseparationT˜nottobeconfusedwithtemperature.Theexpectationvalu

8、eoftheWilsonloopistakeninathermalensemble.TheaboveformulaisdefinedforT˜≫rlarge.OfcourseaswelearnedinapreviouslecturewecancomputeWilsonloopsatlargeλusingtheduality.OnemustfindtheminimalactionstringinthebulkwhichapproachesCrattheboundary.Thentheexpectati