a general brst approach to string theories with zeta function regularizations

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1、G¨oteborgITP98-2,DAMTP-98-21,HKS-NT-FR-98/2-SE31March1998(Revised22March1999)AgeneralBRSTapproachtostringtheorieswithzetafunctionregularizationsStephenHwang1,KarlstadUniversityS-65188Karlstad,SwedenRobertMarnelius2,ITP,ChalmersUniversityofTechnologyG¨oteborg

2、UniversityS-41296G¨oteborg,SwedenPanagiotisSaltsidis3DAMTP,UniversityofCambridgeSilverSt,CambridgeCB39EW,UKarXiv:hep-th/9804003v222Mar1999AbstractWeproposeanewgeneralBRSTapproachtostringandstring-liketheorieswhichhaveawiderrangeofapplicabilitythane.g.theconv

3、entionalconformalfieldtheorymethod.Themethodinvolvesasimplegeneralregularizationofallbasiccommutatorswhichmakesalldivergentsumstobeexpressibleintermsofzetafunctionsfromwhichfinitevaluesthenmaybeextractedinarigorousmanner.Themethodisparticularusefulinordertoinv

4、estigatepossiblestatespacerepresentationstoagivenmodel.Themethodisappliedtothreestringmodels:Theordinarybosonicstring,thetensionlessstringandtheconformaltensionlessstring.Wealsoinvestigatedifferentstatespacesforthesemodels.Thetensionlessstringmodelsaretreated

5、indetails.Althoughwemostlyrederiveknownresultstheyappearinanewfashionwhichdeepensourunderstandingofthesemodels.Furthermore,webelievethatourtreatmentismorerigorousthanmostofthepreviousones.Inthecaseoftheconformaltensionlessstringwefindanewsolutionford=4.1E-mai

6、l:Stephen.Hwang@hks.se2E-mail:tferm@fy.chalmers.se3E-mail:P.Saltsidis@damtp.cam.ac.uk1Introductionandpresentationofthemethod.TheusualoperatorformulationofBRSTquantizationofstringtheoriesarebasedonthefollowingingredients:FirstspecifyaBRSTinvariantvacuumstatea

7、ndthennormalordertheBRSToperatorinordertofinallycheckinwhichdimensiontheBRSToperatorisnilpotent[1].Eventheconformalfieldtheorymethodisbasedontheseingredients[2].Thesemethodshavebeenverysuccessfulwhenappliedtoconventionalstringtheories.However,therearemodelstow

8、hichthesemethodsarenotapplicable.Wehavee.g.thetensionlessstringmodelswhichdonothaveaconventionalvacuumstate[3,4].InthispaperwepresentanewrigorousandverygeneralapproachtotheoperatorversionofBRSTq