Large N gauge theories -- Numerical results(2)

Some physical results in four dimensional large N gauge theories on a periodic torus are summarized.

2

symmetryisbroken.Thecontinuumlimitisobtainedbygoingtothetop-rightcornerofFig.1anddi erentapproachestothiscornerwillresultinoneofthe vecontinuumphases.

The0h-phasepresentforb<0.36forallLisanunphysicalphasethatdoesnotsurvivethecontinuumlimit.The0hto0ctransitionisassoci-atedwiththesingleplaquetteoperatoropeningupagaparoundπinitseigenvaluedistribution.Gauge eldscomeindisconnectedpiecesinalltheXc-phasesduetothepresenceofthegapinthesingleplaquetteoperator5.

The0c-phaseisthecon nedphaseoflargeNQCDandthe1c-phaseisthedecon nedphaseandlc=1/tc.Animmediateconsequenceofcon-tinuumreductionisthatlargeNQCDdoesnotfeeltemperaturesbelowtc6.Numericalanalysishasshownthatlatticespacinge ectsaresmallinthe0c-phaseanditissu cienttoworkatL～9andN～30toextractcontinuumresults.Therefore,numericalcomputationscanbeperformedonaserialcomputerandaclusterofcomputerscanbee cientlyusedtogeneratestatisticsinaMonte-Carlocalculation.