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1、IntroductiontoHolographicSuperconductorsGaryT.HorowitzAbstractTheselecturesgiveanintroductiontothetheoryofholographicsuper-conductors.Thesearesuperconductorsthathaveadualgravitationaldescriptionusinggauge/gravityduality.Afterintroducingasuitablegravitationaltheory,wediscussitspropertiesinvarious
2、regiemes:theprobelimit,theeffectsofbackre-action,thezerotemperaturelimit,andtheadditionofmagneticfields.Usingthegauge/gravitydictionary,thesepropertiesreproducemanyofthestandardfeaturesofsuperconductors.Somefamiliaritywithgauge/gravitydualityisassumed.Alistofopenproblemsisincludedattheend.1Introd
3、uctionThename“holographicsuperconductor”suggeststhatonecanlookatatwo(spa-tial)dimensionalsuperconductorandseeathreedimensionalimage.Wewillseethatthereisaclassofsuperconductorsforwhichthisistrue,buttheimageone“sees”isquitestriking.Itinvolvesachargedblackholewithnontrivial“hair”.Thisremarkableconn
4、ectionbetweencondensedmatterandgravitationalphysicswasdis-coveredjustafewyearsago.Itgrewoutofthegauge/gravitydualitywhichhasemergedfromstringtheory[47,21,61].Althoughthisdualitywasfirstformulatedasaequivalencebetweenacertaingaugetheoryandatheoryofquantumgrav-ity(andprovidednewinsightsintoeachofth
5、esetheories),overthepastdecadeithasbeenappliedwithnotablesuccesstootherareasofphysicsaswell.ManyarXiv:1002.1722v2[hep-th]17Feb2010ofthesenewapplicationsarediscussedinotherlecturesinthisschool.Iwillfo-cusontheapplicationtosuperconductivity.Theselectureswillbeheavilybasedon[29,30,37,38].Foramorege
6、neraldiscussionofapplyinggauge/gravitydualityGaryT.HorowitzPhysicsDepartment,UCSB,SantaBarbara,CA93106,USA,e-mail:gary@physics.ucsb.edu12GaryT.Horowitztocondensedmatter,seetheexcellentreviewsbyHartnoll[27],Herzog[32]andMcGreevy[48].Iwillstartwithabriefintroductiontosuperconductivity.Insection2,I
7、willintroduceasimplemodelforaholographicsuperconductor.Mostofourdiscussionwillbedevotedtoexploringtheconsequencesofthismodel,beginninginsection3withtheprobelimit-asimplificationofthemodelwhichpreservesmostofthephysics.Insecti
