资源描述：
《Normal coordinates in Riemannian and Kahler geometry》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
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)canbedefinedasholomorphiccoordinates.WeprovethatKNCtransformasarXiv:hep-t
3、h/0203081v317Jun2002aholomorphictangentvectorunderholomorphiccoordinatetransformations,andthereforethattheyarenaturalextensionsofRNCtothecaseofK¨ahlermanifolds.TheKNCexpansionprovidesamanifestlycovariantbackgroundfieldmethodpreservingthecomplexstructureinsuper
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].Theyaredefinedascoordinatesalonggeodesiclinesstartingfromachosenpoint.Hence,anypointinapatchofRNChas
6、one-to-onecorrespondencewithatangentvectoratthechosenpoint.Inmostsuperstringtheories,extradimensionsofthehigher-dimensionalspace-timearecompactifiedtoaCalabi-Yaumanifold[4],whichisaRicci-flatK¨ahlermanifold.Thiscanbedescribedbyconformallyinvariantsupersymmetric
7、nonlinearsigmamodelsintwodimensions,whosetargetspacesareK¨ahlermanifolds[5].Forperturbative(ornon-perturbative)analyses,weneedtoexpandtheLagrangianintermsoffluctuatingfieldsaroundthebackgroundfields[6].Agenerallycovariantexpansionthatpreservesthecomplexstructure
8、ofthetargetspaceismostsuitableintheseanalyses.RNCprovideagenerallycovariantexpansion,buttheyarenotholomorphic,whereasK¨ahlernormalcoordinates(KNC)giveussuchanexpan-sion[7].KNCaredefinedasc
