Large N gauge theories -- Numerical results

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

February1,200823:52WSPC-ProceedingsTrimSize:9inx6intalk

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002 luJ 02 1v941706/0ht-pe:hviXra1

LargeNgaugetheories–Numericalresults

R.Narayanan

DepartmentofPhysics,FloridaInternationalUniversity,

Miami,FL33199,USA

E-mail:rajamani.narayanan@ u.edu

H.Neuberger

RutgersUniversity,DepartmentofPhysicsandAstronomy,

Piscataway,NJ08855,USA

E-mail:neuberg@physics.rutgers.edu

SomephysicalresultsinfourdimensionallargeNgaugetheoriesonaperiodictorusaresummarized.

Keywords:LargeNQCD,decon nement,phasetransitions.

1.Introduction

tticeQCDisausefultechniqueforextractingfundamentalresultsinthelargeNlimitofQCD.Fermionsarenaturallyquenchedinthe’tHooftlimitoflargeNQCDandthissigni cantlyreducesthecomputationalcostinalatticecalculation.Inaddition,thereisaconceptofcontinuumreduction3,namely,physicsdoesnotdependonthesizeofboxl4forl>lcandlcisaphysicalcriticalsize.ThesetwoobservationshavebeenusedtoextractphysicalresultsinthelargeNlimitofQCDusingnumericaltechniquesonthelattice.

2.PhasesoflargeNQCD

LargeNQCDonacontinuumtorusl4hasseveralphases4dependinguponthesizeofthetorusasshowninFig.1.ThecontinuumactionhasU4(1)symmetriesassociatedwiththePolyakovloopsinthefourdirectionsandthevariousphasescorrespondtothenumberofdirectionsinwhichthis