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1、NuclearPhysicsB234(1984)173-188©North-HollandPublishingCompanyRESTRICTIONSONSYMMETRYBREAKINGINVECTOR-LIKEGAUGETHEORIES*C.VAFAandE.WITTENJosephHenryLaboratories,PrincetonUniversity,Princeton,NewJersey08544,USAReceived26August1983Modulosomehighlyplausibleassumptions,weshowt
2、hatvector-likeglobalsymmetries(likeisospinorbaryonnumber)arenotspontaneouslybrokeninvector-likegaugetheorieswith0=0(likeQCD).Wealsoshowthatinthesetheoriesmasslessboundstatesdonotformfrommassiveconstituents.Anoutstandingproblemaboutstronglyinteractinggaugetheoriesistodeter
3、minewhichglobalsymmetriesarespontaneouslybrokenandwhichareunbroken.Exist-ingresultsarebasedonlatticetheories[1],roughdynamicalapproximations[2],considerationsofanomalies[3],andthe1/Nexpansion[4].Forareviewofthesubjectseeref.[5].ConventionalQCDisanexampleofaspecialclassoft
4、heories:theoriesinwhichtheonlyinteractionsarevector-likegaugeforcesandinwhichallCP-violatingvacuumanglesvanish.Forthesetheoriesthereisadefiniteconven-tionalwisdom,accordingtowhichthevectorsymmetriesoffermionsareallunbroken,whiletheaxialvector(chiral)symmetriesareallsponta
5、neouslybrokeninthezero-masslimit.Inthispaperwewillshow,modulosomehighlyplausibletechnicalassumptions,thatthefirstpartoftheconventionalwisdomistrue:invector-likegaugetheories,vectorsymmetriesarenotspontaneouslybroken.Giventhevalidityofthefirstpartoftheconventionalwisdom,th
6、eanomalyconditions[3]stronglysuggestthatthesecondpartisalsovalidinmostorallcases.Anotherimportantquestionaboutstronglyinteractinggaugetheoriesistode-terminethequantumnumbersofthemasslessfermionboundstates,ifany.Inthisregardanaturalquestionarises.Canamasslessboundstatebema
7、defromconstituentssomeofwhichhaveanon-zerobaremass?Inotherwords,cantheattractiveforcecancelthebaremassesoftheconstituents?Itisknownthat,ingeneral[6,7],inquantumfieldtheorymassiveconstituentscanbeboundintomasslessboundstates.Howeverwewillshowthatinparity-conserving,vector-
8、liketheoriesthisisnotpossible;allconstituentsofamasslesscompositemusthavezero*Supportedinpartbyt
