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时间:2019-03-07
《loop equations for the d-dimensional n-hermitian matrix model》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
1、LoopEquationsforthed-dimensionaln-HermitianMatrixmodelJorgeAlfaroFacultaddeF´ısicaUniversidadCat´olicadeChileCasilla306,Santiago22,Chilejalfaro@lascar.puc.clNovember81993AbstractWederivetheloopequationsforthed-dimensionaln-Hermitianmatrixmodel.Theseareaconseq
2、uenceoftheSchwinger-Dysonequa-tionsofthemodel.MoreoverweshowthatinleadingorderoflargeNtheloopequationsformaclosedset.Inparticularwederivetheloopequationsforthen=2kmatrixmodelrecentlyproposedtode-scribethecouplingofTwo-dimensionalquantumgravitytoconformalmatte
3、rwithc>1.arXiv:hep-th/9311086v116Nov1993PUC-FIS28-93November199301IntroductionThelastthreeyearshaveseenarapiddevelopmentintheknowledgerelativetotwo-dimensionalquantumgravitycoupledtoconformalmatterwithc≤1.Thishasbeenpossiblebytheuseofmatrixmodeltechniquesandt
4、helargeNexpansion,combinedwiththedoublescalinglimit[1]Veryrecentlyanewinterpretationofthedoublescalinglimitasafinitesizerescalinghasemerged[2][3]basedontherenormalizationgroupappliedtolargeNmodels[4][5].Althoughthenewtechniqueshaveprovidedaverydeepunderstandin
5、goftwo-dimensionalquantumgravitycoupledtoc≤1conformalmatter,abarrierhasemergedatc=1,avoidingthecontinuationofthepreviousresultsbeyondthispoint.Thesamebarrierappearsinthecontinuumtreatmentofnon-criticalstrings.[6]Variousapproachestosurpassthisproblemhavebeensu
6、ggested.Amongthemwementiontheuseofreducedmodelstodiscussthed-dimensionalmatrixmodel[7]whichistherightmodeltodiscussthed-dimensionalstring,VeryrecentlywehaveobtainedtheloopequationsforthismodelforarbitraryNandshowthattheyformaclosedsetinleadingorderoflargeN[8]
7、.Forthemomenttheyhavenotbeensolvedbutweseethemasanimportantexactresultthatmaypermittocrossthebarrieratc=1.Lastyeara2n-Hermitianmatrixmodelinzerodimensionshavebeenproposedtodescribeasystemwithc=n/2coupledto2dgravity[9].Soasolutionofthismodelisanotherwaytocross
8、thebarrier.Fouryearsagoweobtainedtheloopequationsforthezerodimensionaltwo-matrixmodel[10],extendingthesolutionofMethaforthepartitionfunction[11].Lastyearwewereabletosolvetheseequationscom
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