The theta dependent of pure gauge theories in four dimensions can be studied using a duality of large N gauge theories with string theory on a certain spacetime. Via this duality, one can argue that for every theta, there are infinitely many vacua that are
hep-th/9807109,IASSNS-HEP-98-65
ThetaDependenceinTheLargeNLimit
arXiv:hep-th/9807109v1 15 Jul 1998OfFour-DimensionalGaugeTheoriesEdwardWittenSchoolofNaturalSciences,InstituteforAdvancedStudyOldenLane,Princeton,NJ08540,USATheθdependenceofpuregaugetheoriesinfourdimensionscanbestudiedusingadualityoflargeNgaugetheorieswithstringtheoryonacertainspacetime.Viathisduality,onecanarguethatforeveryθ,therearein nitelymanyvacuathatarestableinthelargeNlimit.Thetruevacuum,foundbyminimizingtheenergyinthisfamily,isasmoothfunctionofθexceptatθ=πwhereitjumps.ThisjumpisassociatedwithspontaneousbreakingofCPsymmetry.Domainwallsseparatingadjacentvacuaaredescribedintermsofwrappedsixbranes.
July,1998
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