Phase Transition of 4D Simplicial Quantum Gravity with U(1) Gauge Field

The phase transition of 4D simplicial quantum gravity coupled to U(1) gauge fields is studied using Monte-Carlo simulations. The phase transition of the dynamical triangulation model with vector field ($N_{V}=1$) is smooth as compared with the pure gravity

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991 epS 6 2v8408099/tal-pe:hviXraPhaseTransitionof4DSimplicialQuantumGravitywithU(1)GaugeField

H.S.Egawa

a,b

,S.Horatab,a,N.TsudabandT.Yukawa

c,b

a

DepartmentofPhysics,TokaiUniversity,Hiratsuka,Kanagawa259-1292,Japan

b

TheoryDivision,InstituteofParticleandNuclearStudies,KEK,HighEnergyAcceleratorResearchOrganization,Tsukuba,Ibaraki305-0801,Japan

c

CoordinationCenterforResearchandEducation,TheGraduateUniversityforAdvancedStudies,Hayama,Miura,Kanagawa240-0193,Japan

Thephasetransitionof4DsimplicialquantumgravitycoupledtoU(1)gauge eldsisstudiedusingMonte-Carlosimulations.Thephasetransitionofthedynamicaltriangulationmodelwithavector eld(NV=1)issmoothcomparedwithpuregravity(NV=0).Thenodesusceptibility(χ)isstudiedbythe nitesizescalingmethod.Atthecriticalpoint,thenodedistributionhasasharppeakincontrasttothedoublepeakinpuregravity.Fromthenumericalresults,weexpectthat4DsimplicialquantumgravitywithU(1)vector eldshasahigherorderphasetransitionthan1storder,whichmeansthepossibilitytotakethecontinuumlimitatthecriticalpoint.

1.Introduction

Thephasestructureof4Dpuresimplicialquan-tumgravityhasbeenintensivelyinvestigated.In4Dpuregravity,twodistinctphasesareknown.Forsmallvaluesofthebaregravitationalcou-plingconstantthesystemisintheso-calledelon-gatedphase,whichhasthecharacteristicsofabranchedpolymer.Forlargevaluesofthebaregravitationalcouplingconstantitisintheso-calledcrumpledphase.Numerically,thephasetransitionbetweenthetwophaseshasbeenshowng(Λ

1

tobe1storder[1,2].Asaresult,itisdi culttoconstructacontinuumtheory.Ournextstepistoinvestigateanextendedmodelof4Dquantumgravity.Recentlythephasestructureoftheex-tendedmodelsof4Dquantumgravityhasbeenstudiednumerically[3,4].Inamodelwithvector elds,theintermediatephasehasbeenobservedbetweenthecrumpledphaseandtheelongatedphase.Weconsiderthepossibilityofacontinuumlimitatthecriticalpoint.Inordertoinvestigatethephasetransition,wemeasurethe nitesizescalingofnodesusceptibility(χ),

χ=(<N02

> <N0>2)/N4,

(1)

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