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1、hep-th/9803265CERN-TH/98-83HUTP-98/A008ITEP-TH.8/98NSF-ITP-98-031YCTP-P6/98D-particleboundstatesandgeneralizedinstantonsGregoryMoore,1NikitaNekrasov,2,3andSamsonShatashvili1,4*1DepartmentofPhysics,YaleUniversity,NewHaven,CT06520,Box208120,USA2InstituteofTheoreticalandExperimentalPhysics
2、,117259,Moscow,Russia3LymanLaboratoryofPhysics,HarvardUniversity,Cambridge,MA02138,USA4TheoryDivision,CERN,CH-1211,Geneve23,Switzerlandmoore@castalia.physics.yale.edunikita@string.harvard.edusamson@euler.physics.yale.eduarXiv:hep-th/9803265v320Apr1998Wecomputetheprincipalcontributiontot
3、heindexinthesupersymmetricquantumme-chanicalsystemswhichareobtainedbyreductionto0+1dimensionsofN=1,D=4,6,10super-Yang-MillstheorieswithgaugegroupSU(N).Theresultsare:1forD=4,6,N2P1forD=10.WealsodiscusstheD=3case.d
4、Nd2March31,1998*OnleaveofabsencefromSt.PetersburgBranchofSteklovMathematic
5、alInstitute,Fontanka,St.Petersburg,Russia.1.IntroductionTheexistenceofM-theorydependscruciallyontheexistencewithintype-IIAstringtheoryofatowerofmassiveBPSparticleselectricallychargedwithrespecttotheRR1-form.Theseparticles,originallydescribedasblackholesinIIAsupergravity[1],canbeinterpre
6、tedasKaluza-Kleinparticlesofeleven-dimensionalM-theorycompactifiedonacircle[2][3].Later,theseparticleswereidentifiedwith“D0-branes”[4].IntheD-braneformulationitbecomesclearthatincertainenergyregimesthedynamicsofNsuchparticlescanbedescribedbythesupersymmetricquantummechanicsofN×NHermitianm
7、atricesobtainedfromdimensionalreductionofN=1,D=10super-Yang-Millstheory[5](thequantummechanicalmodelwasoriginallystudiedin[6]).TheexistenceoftheM-theoreticKaluza-KleintowerofstatesisequivalenttothestatementthatthisquantummechanicshasexactlyoneboundstateforeachN.Consequently,provingtheex
8、istenceoftheseboundstateshasbeenthefocusofseveralrecentpapersofwhich[7][8][9]arethemostrelevanttothepresentwork.Inparticular,wenotethattheexistenceoftheboundstateinthecaseofN=2wasprovenin[7],butthecaseN>2remainsopen.TheresultsofthepresentpaperwillhelpcompletetheproofforallN.The
