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Discrete Torsion in Singular G_2-Manifolds and Real LG

We investigate strings at singularities of G_2-holonomy manifolds which arise in Z_2 orbifolds of Calabi-Yau spaces times a circle. The singularities locally look like R^4/Z_2 fibered over a SLAG, and can globally be embedded in CICYs in weighted projectiv

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a c2002InternationalPressAdv.Theor.Math.Phys.6(2002)207–278DiscreteTorsioninSingularG2-ManifoldsandRealLGRaduRoibanChristianR¨omelsbergerJohannesWalcherDepartmentofPhysicsDepartmentofPhysicsInstituteforTheoreticalUniversityofCaliforniaandPhysicsSantaBarbara,CA93106,CIT-USCCenterforUniversityofCaliforniaUSATheoreticalPhysicsSantaBarbara,CA93106,roiban@vulcan.physics.ucsb.eduUniversityofSouthernUSACalforniawalcher@itp.ucsb.eduLosAngeles,roemel@http://www.wendangxiazai.comc.eduCA90089,USAAbstractWeinvestigatestringsatsingularitiesofGZ2-holonomymanifolds

whicharisein2orbifoldsofCalabi-Yauspacestimesacircle.ThesingularitieslocallylooklikeR4/Z2 beredoveraSLAG,andcangloballybeembeddedinCICYsinweightedprojectivespaces.Thelocalmodeldependsonthechoiceofadiscretetorsioninthe bration,andtheglobalmodelonananti-holomorphicinvolutionoftheCalabi-Yauhypersurface.WedeterminehowthesechoicesarerelatedtoeachotherbycomputingaWilsonsurfacedetectingdiscretetorsion.Wethenfollowthesameorbifoldstothenon-geometricLandau-Ginzburgregionofmodulispace.Wearguethatthesymmetry-breakingtwistedsectorsaree ectivelycapturedbyrealLandau-Ginzburgpotentials.Inparticular,we ndagreementinthelow-energyspectraofstringscomputedfromgeometryandGepner-modelCFT.Alongtheway,weconstructthefullmodulardataoforbifoldsofN=2minimalmod-elsbythemirrorautomorphism,andgiveareal-LGinterpretationoftheirmodularinvariants.Someofthemodelsprovideexamplesofthemirror-symmetryphenomenonforG2holonomy.

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