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1、March1995QMW-TH-95-29.SPECIALGEOMETRYANDTWISTEDMODULIINORBIFOLDTHEORIESWITHCONTINUOUSWILSONLINES.W.A.Sabra*,S.Thomas**andN.Vanegas***DepartmentofPhysics,RoyalHollowayandBedfordNewCollege,UniversityofLondon,Egham,Surrey,U.K.**DepartmentofPhysics,QueenMaryandWest eldCollege,UniversityofLondon,
2、MileEndRoad,LondonE14NS,U.K.ABSTRACTTargetspacedualitysymmetries,whichactsonKahlerandcontinuousWilsonlinemoduli,ofaZ(N6=2)2-dimensionalsubspaceofthemodulispaceoforbifoldNcompacti cationaremodi edtoincludetwistedmoduli.ThesespacesdescribedSU(n;1)bythecosetsarespecialKahler,afactwhichisexploit
3、edinderivingSU(n)U(1)theextensionoftreeleveldualitytransformationtoincludehigherordersofthetwistedmoduli.Also,restrictionsonthesehigherordertermsarederived.Heteroticstringtheoriescompacti edonorbifoldsareofphenomenologicalim-portanceastheygiverisetoanN=1space-timesupersymmetricsemi-realisti
4、cfourdimensionalquantum eldtheories[1,2].Aphenomenologicallyappealingfea-tureofstringcompacti cationsliesinthefactthatthephysicalcouplingsinthelow-energye ectiveactionaredependentonthemoduli eldswhichparametrizetheshapeandsizeoftheorbifoldandpossiblecontinuousWilsonlines.Also,suchanactionhas
5、anovelsymmetryknownastargetspaceduality.Thisisadiscretesymmetryofthemodulispacewhichleavestheunderlyingconformal eldtheoryinvariant.Thissymmetryrestrictsthelowenergye ectiveactionandconnectsittothetheoryofmodularforms[3].Thelow-energyactionisanN=1supergravitycoupledtoYang-Millsandmatter elds
6、.Iftermswithuptotwoderivativesinthebosonic eldsareincluded,thetheoryisthende nedintermsoftheKahlerpotentialKwhichencodesthekinetictermsforthemassless elds,thesuperpo-tentialWcontainingtheYukawacouplingsandthef?functionwhoserealpart,atthetreelevel,determinesthegaugecouplings[13].Infactthelagr
7、angianofthetheorydependsonKandWviathetargetspacedualityinvariantcombination2G=K+logjWj:(1)Themethodofcalculatingthesuperpotentialofthelow-energye ectiveactiondirectlyfromtheunderlyingconformal eldtheorywasgivenin[4].Moreover,theuntwistedmodulidepen
