引力的全息性质与其相关问题的研究

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1、ABSTRACTTheholographichypothesisstatesthataquantumtheoryofgravityind+ldimensionalspacetimemaybewelldescribedbyphysicalobervablesontheddimensionalboundarytotheregion．Inrecentyearsthisproposalhasbeenwellconcemedandwidelybelievedthatitmightbeviewedasafundamental

2、principleforanyquantumtheoryofgravity．Asallimplementofholographicprinciple，AdS／CFTdualitywhichoriginatedformstringtheoryhasbeenwellstudiedandbringssomeimportantachievement．Especially，inthesetwoyearsithasbeenappliedtothestudyofthestronglycorrelatedsystemsinQCD

3、andcondensedmatterphysics．Peoplehaveconstructedholographicmodelswitllagoaltoexploreundisclosedphenomenainhydrodynamics，superconductor,non—Fermionfluid，strangemetalaswellasquantumHalleffects．Moreover,holographicprinciplehasalsobeenappliedtootherfieldssuchashol

4、ographicuniverseandholographicdarkenergyetc．Motivatedbythedevelopmentabove，inthisthesisweconcentrateontheconstructionoftheholographicsuperconductormodelsinquasi—topologicalgravitytheoryandinvestigatetheirproperties．Specifically，byintroducingscalarfieldandYang

5、-MillsgaugefieldinanAdSblackholebackground，westudytheholographics-waveandp-wavesuperconductormodelsrespectively．OurmainresultsandconclusionsCanbesummarizedasfollows．Firstly，inbothmodelsfors-waveandp-wavesuperconductors，theincreaseofthehighercurvaturecouplingp

6、arameterswillmakethecondensationsharder．Secondly，theuniversalrelation咚／乃兰8whichisobtainedintheholographicmodelofEinsteingravityisunstable，anditwillshiftwiththechangesofGBcouplingparameteraswellasthecurvature—cubedinteractionparameter．Finally，theconductivityco

7、mponent盯坩and％havedifferentbehaviorswiththefrequency缈inthep-waveholographicsuperconductor．Thecoherencelengthdependsonthecouplingparameteraswell．Keywords：blackhole；holographicprinciple；AdS／CFTduality；ABSTRACTholographicsuperconductors．IV第一章引言1．1研究背景和意义关于引力的本质和基

8、本性质的探讨是一门十分古老的学科。它的发展经历了从牛顿的经典引力理论刭爱因斯坦的狭义相对论以至广义相对论的巨大转变和挑战。1917年诞生的广义相对论认为，物质的存在使得时空弯曲，万有引力即时空弯曲的表现。在时空弯曲很厉害处，时空几何的性质将发生重要的改变，这就形成黑洞，它是广义相对论必然的结果。随着广义相对论的不断被实验验证，人们对引力本质的认识上升到一个新的阶段，在此基