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1、CondensedmatterandAdS/CFTSubirSachdevLecturesatthe5thAegeansummerschool,“Fromgravitytothermalgaugethe-ories:theAdS/CFTcorrespondence”,Adamas,MilosIsland,Greece,September21-26,2009,andtheDeSitterLectureSeriesinTheoreticalPhysics2009,UniversityofGroningen,
2、November16-20,2009.AbstractIreviewtwoclassesofstrongcouplingproblemsincondensedmatterphysics,anddescribeinsightsgainedbyapplicationoftheAdS/CFTcorrespon-dence.Thefirstclassconcernsnon-zerotemperaturedynamicsandtransportinthevicinityofquantumcriticalpoints
3、describedbyrelativisticfieldtheories.Ide-scribehowrelativisticstructuresariseinmodelsofphysicalinterest,presentre-sultsfortheirquantumcriticalcrossoverfunctionsandmagneto-thermoelectrichy-drodynamics.Thesecondclassconcernssymmetrybreakingtransitionsoftwo-
4、dimensionalsystemsinthepresenceofgaplesselectronicexcitationsatisolatedpointsoralonglines(i.e.Fermisurfaces)intheBrillouinzone.Idescribethescal-ingstructureofarecenttheoryoftheIsing-nematictransitioninmetals,anddiscussitspossibleconnectiontotheoriesofFer
5、misurfacesobtainedfromsimpleAdSdu-arXiv:1002.2947v1[hep-th]16Feb2010als.SubirSachdevDepartmentofPhysics,HarvardUniversity,CambridgeMA02138,e-mail:sachdev@physics.harvard.edu12SubirSachdev1IntroductionThepastcoupleofdecadeshaveseenvigoroustheoreticalactiv
6、ityonthequantumphasesandphasetransitionsofcorrelatedelectronsystemsintwospatialdimen-sions.Muchofthisworkhasbeenmotivatedbythecupratesuperconductors,butthelistofinterestingmaterialscontinuestoincreaseunabated[1].Methodsfromfieldtheoryhavehadastrongimpacto
7、nmuchofthiswork.In-deed,theyhavebecomepartofthestandardtoolkitofcondensedmatterphysicists.Intheselectures,Ifocusontwoclassesofstrong-couplingproblemswhichhavenotyieldedaccuratesolutionsviatheusualarsenaloffield-theoreticmethods.IwillalsodiscusshowtheAdS/C
8、FTcorrespondence,discoveredbystringtheorists,hasalreadyallowedsubstantialprogressonsomeoftheseproblems,andoffersencour-agingprospectsforfutureprogress.Thefirstclassofstrong-couplingproblemsareassociatedwiththereal-time,fi-ni
