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1、IASSNS-HEP-99/74hep-th/9908142StringTheoryandNoncommutativeGeometryNathanSeibergandEdwardWittenSchoolofNaturalSciencesInstituteforAdvancedStudyOldenLane,Princeton,NJ08540WeextendearlierideasabouttheappearanceofnoncommutativegeometryinstringtheorywithanonzeroB-eld.Weidentifyalimi
2、tinwhichtheentirestringdynamicsisdescribedbyaminimallycoupled(supersymmetric)gaugetheoryonanoncommutativespace,anddiscussthecorrectionsawayfromthislimit.Ouranalysisleadsustoanequivalencebetweenordinarygaugeeldsandnoncommutativegaugeelds,whichisrealizedbyachangeofvariablesthatcan
3、bedescribedexplicitly.ThischangeofvariablesischeckedbycomparingtheordinaryDirac-Born-Infeldtheorywithitsnoncommutativecounterpart.arXiv:hep-th/9908142v330Nov1999Weobtainanewperspectiveonnoncommutativegaugetheoryonatorus,itsT-duality,andMoritaequivalence.WealsodiscusstheD0=D4syst
4、em,therelationtoM-theoryinDLCQ,andapossiblenoncommutativeversionofthesix-dimensional(2;0)theory.8/991.IntroductionTheideathatthespacetimecoordinatesdonotcommuteisquiteold[1].Ithasbeenstudiedbymanyauthorsbothfromamathematicalandaphysicalperspective.Thetheoryofoperatoralgebrashasb
5、eensuggestedasaframeworkforphysicsinnoncommutativespacetime{see[2]foranexpositionofthephilosophy{andYang-Millstheoryonanoncommutativetorushasbeenproposedasanexample[3].Thoughthisexampleatrstsightappearstobeneithercovariantnorcausal,ithasprovedtoariseinstringtheoryinadenitelimit[
6、4],withthenoncovariancearisingfromtheexpectationvalueofabackgroundeld.Thisanalysisinvolvedtoroidalcompactication,inthelimitofsmallvolume,withxedandgenericvaluesoftheworldsheetthetaangles.ThislimitisfairlynaturalinthecontextofthematrixmodelofM-theory[5,6],andtheoriginaldiscussion
7、wasmadeinthiscontext.Indeed,earlyworkrelatingmembranestolargematrices[7],hasmotivatedin[8,9]constructionssomewhatsimilarto[3].Forotherthoughtsaboutapplicationsofnoncommutativegeometryinphysics,seee.g.[10].Noncommutativegeometryhasalsobeenusedasaframeworkforopenstringeldtheory[11
8、].Partofthebeautyoftheanalysisin[4]wasthatT-dua
