Lectures on Holographic Superfluidity and Superconductivity

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1、PUPT-2297LecturesonHolographicSuper uidityandSuperconductivityC.P.HerzogDepartmentofPhysics,PrincetonUniversity,Princeton,NJ08544,USA(Dated:March26,2009)FourlecturesonholographyandtheAdS/CFTcorrespondenceappliedtocondensedmattersystems.1Therstlectur

2、eintroducestheconceptofaquantumphasetransition.ThesecondlecturediscusseslinearresponsetheoryandWardidentities.ThethirdlecturepresentstransportcoecientsderivedfromAdS/CFTthatshouldbeapplicableinthequantumcriticalregionassociatedtoaquantumphasetransit

3、ion.Thefourthlecturebuildsinthephysicsofasuperconductingorsuper uidphasetransitiontothesimpleholographicmodelofthethirdlecture.I.INTRODUCTION:QUANTUMPHASETRANSITIONSSpurredbytheconcreteproposalofrefs.[1{3]foranAdS/CFTcorrespondence,therearesomegoodre

4、asonswhyholographicideashavebecomesoimportantinhighenergytheoreticalphysicsoverthelasttenyears.TherstandperhapsmostfundamentalreasonisthattheAdS/CFTconjectureprovidesadenitionofquantumgravityinaparticularcurvedbackgroundspace-time.ThesecondisthatAd

5、S/CFTprovidesatoolforstudyingstronglyinteractingeldtheories.Theselecturesconcernthemselveswiththesecondreason,butIwillspendaparagraphontherst.Giventhelackofalternativedenitionsofquantumgravity,theAdS/CFTconjectureisdi-culttoprove,butthecorrespond

6、encedoesgiveadenitionoftypeIIBstringtheoryinaxedtendimensionalbackgroundandbyextensionoftypeIIBsupergravity.RecallthattheoriginalconjecturepositsanequivalencebetweentypeIIBstringtheoryinthespace-timeAdS5S5andthemaximallysupersymmetric(SUSY)SU(N)Ya

7、ng-Millstheoryin3+1dimensions.(Inournota-tion,AdS5isvedimensionalanti-deSitterspaceandS5isavedimensionalsphere.)Yang-Millstheory,atleastinprinciple,canbesimulatedonacomputerasthecontinuumlimitofalatticetheory.ThelowenergylimitoftypeIIBstringtheoryi

8、stypeIIBsupergravityandthecorrespon-dencemustalsoyieldaquantumtheoryofgravity.ThislineofreasoninghasledtoanimprovedarXiv:0904.1975v2[hep-th]27Jul2009understandingofblackholephysics,includingatentativeresolutionoftheblackholeinformationparadoxandabett