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1、NBI-HE-99-17hep-th/9907140July1999CONSTRUCTINGD-BRANESFROMK-THEORYKasperOlsena;1andRichardJ.Szaboa;baTheNielsBohrInstituteBlegdamsvej17,DK-2100Copenhagen ,DenmarkbDepartmentofPhysicsandAstronomy,UniversityofBritishColumbia6224AgriculturalRoad,Vancouver,B.C.V6T1Z1,Canada
2、kolsen,szabo@nbi.dkAbstractAdetailedreviewofrecentdevelopmentsinthetopologicalclassi cationofD-branesinsuperstringtheoryispresented.Beginningwithathorough,self-containedintro-ductiontothetechniquesandapplicationsoftopologicalK-theory,therelationshipsbetweentheclassiccon
3、structionsofK-theoryandtherecentrealizationsofD-branesastachyonicsolitons,comingfromboundstatesofhigherdimensionalsystemsofunstablebranes,aredescribed.ItisshownhowtheK-theoryformalismnaturallyreproducestheknownspectraofBPSandnon-BPSD-branes,andhowitcanbearXiv:hep-th/990
4、7140v26Aug1999systematicallyusedtopredicttheexistenceofnewstates.TheemphasisisplacedonthenewinterpretationsofD-branesasconventionaltopologicalsolitonsinotherbraneworldvolumes,howthemathematicalformalismcanbeusedtodeducethegauge eldcontentonbothsupersymmetricandnon-BPSbr
5、anes,andalsohowK-theorypredictsnewrelationshipsbetweenthevarioussuperstringtheoriesandtheirD-branespectra.Theimplementationsofdualitysymmetriesasnaturaliso-morphismsofK-groupsarediscussed.Therelationshipwiththestandardcohomo-logicalclassi cationispresentedandusedtoderiv
6、eanexplicitformulaforD-branecharges.SomestringtheoreticalconstructionsoftheK-theorypredictionsarealsobrie
ydescribed.1AddressafterSeptember1,1999:LymanLaboratoryofPhysics,HarvardUniversity,Cambridge,MA02138,U.S.A.Contents1IntroductionandOverview31.1Outline..............
7、........................92ElementsofTopologicalK-Theory112.1TheGrothendieckGroup............................122.2TheGroupK(X)................................132.3ReducedK-Theory...............................152.4HigherK-TheoryandBottPeriodicity....................162.5
8、MultiplicativeStructures............................182.6RelativeK-Theory...............................202.7C
