matrix quantum mechanics and 2-d string theory [thesis] - s. alexandrov

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1、ServicedePhysiqueTh´eorique–C.E.A.-SaclayUNIVERSITEPARISXI´PhDThesisMatrixQuantumMechanicsandTwo-dimensionalStringTheoryinNon-trivialBackgroundsSergeiAlexandrovarXiv:hep-th/0311273v24Dec2003AbstractStringtheoryisthemostpromisingcandidateforthetheoryunifyingallinteractionsinclud

2、inggravity.Ithasanextremelydifficultdynamics.Therefore,itisusefultostudysomeitssimplifications.Oneofthemisnon-criticalstringtheorywhichcanbedefinedinlowdimensions.Aparticularinterestingcaseis2Dstringtheory.Ontheonehand,ithasaveryrichstructureand,ontheotherhand,itissolvable.Acomplet

3、esolutionof2DstringtheoryinthesimplestlineardilatonbackgroundwasobtainedusingitsrepresentationasMatrixQuantumMechanics.ThismatrixmodelprovidesaverypowerfultechniqueandrevealstheintegrabilityhiddenintheusualCFTformulation.Thisthesisextendsthematrixmodeldescriptionof2Dstringtheor

4、ytonon-trivialback-grounds.WeshowhowperturbationschangingthebackgroundareincorporatedintoMatrixQuantumMechanics.TheperturbationsareintegrableandgovernedbyTodaLatticehier-archy.Thisintegrabilityisusedtoextractvariousinformationabouttheperturbedsystem:correlationfunctions,thermod

5、ynamicalbehaviour,structureofthetargetspace.Theresultsconcerningtheseandsomeotherissues,likenon-perturbativeeffectsinnon-criticalstringtheory,arepresentedinthethesis.AcknowledgementsThisworkwasdoneattheServicedePhysiqueTh´eoriqueducentred’´etudesdeSaclay.Iwouldliketothankthelabo

6、ratoryfortheexcellentconditionswhichallowedtoaccomplishmywork.AlsoIamgratefultoCEAforthefinancialsupportduringthesethreeyears.Equally,mygratitudeisdirectedtotheLaboratoiredePhysiqueTh´eoriquedel’EcoleNor-maleSup´erieurewhereIalsohadthepossibilitytoworkallthistime.Iamthankfultoal

7、lmembersofthesetwolabsforthenicestimulatingatmosphere.Especially,Iwouldliketothankmyscientificadvisers,VolodyaKazakovandIvanKostovwhoopenedanewdomainoftheoreticalphysicsforme.Theircreativityanddeepknowledgeweredecisiveforthesuccessofourwork.Besides,theircareinallproblemshelpedme

8、muchduringtheseyearsoflifeinFrance.Iamgratefultoallsci