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《Normal coordinates in Riemannian and Kahler geometry》由會(huì)員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫(kù)。
1、OU-HET407PURD-TH-02-02hep-th/0203081March2002NormalCoordinatesinK¨ahlerManifoldsandtheBackgroundFieldMethodKiyoshiHigashijima1?,EtsukoItou1?andMunetoNitta2?1DepartmentofPhysics,GraduateSchoolofScience,OsakaUniversity,Toyonaka,Osaka560-0043,Japan2DepartmentofP
2、hysics,PurdueUniversity,WestLafayette,IN47907-1396,USAAbstractRiemannnormalcoordinates(RNC)areunsuitableforK¨ahlermanifoldssincetheyarenotholomorphic.Instead,K¨ahlernormalcoordinates(KNC)canbede?nedasholomorphiccoordinates.WeprovethatKNCtransformasarXiv:hep-t
3、h/0203081v317Jun2002aholomorphictangentvectorunderholomorphiccoordinatetransformations,andthereforethattheyarenaturalextensionsofRNCtothecaseofK¨ahlermanifolds.TheKNCexpansionprovidesamanifestlycovariantbackground?eldmethodpreservingthecomplexstructureinsuper
4、symmetricnonlinearsigmamodels.?E-mail:higashij@phys.sci.osaka-u.ac.jp?E-mail:itou@het.phys.sci.osaka-u.ac.jp?E-mail:nitta@physics.purdue.edu1IntroductionTheequivalenceprincipleassertsthatgeneralcoordinatetransformationsoncurvedspace-timesdonotalteranyphysics,
5、sothatonecanconsiderthecoordinatesthatmakeagivenapplicationthesimplest.Riemannnormalcoordinates(RNC)repre-sentonesuchsetofcoordinatesforRiemannmanifolds[1,2,3].Theyarede?nedascoordinatesalonggeodesiclinesstartingfromachosenpoint.Hence,anypointinapatchofRNChas
6、one-to-onecorrespondencewithatangentvectoratthechosenpoint.Inmostsuperstringtheories,extradimensionsofthehigher-dimensionalspace-timearecompacti?edtoaCalabi-Yaumanifold[4],whichisaRicci-?atK¨ahlermanifold.Thiscanbedescribedbyconformallyinvariantsupersymmetric
7、nonlinearsigmamodelsintwodimensions,whosetargetspacesareK¨ahlermanifolds[5].Forperturbative(ornon-perturbative)analyses,weneedtoexpandtheLagrangianintermsof?uctuating?eldsaroundthebackground?elds[6].Agenerallycovariantexpansionthatpreservesthecomplexstructure
8、ofthetargetspaceismostsuitableintheseanalyses.RNCprovideagenerallycovariantexpansion,buttheyarenotholomorphic,whereasK¨ahlernormalcoordinates(KNC)giveussuchanexpan-sion[7].KNCarede?nedasc
