您好,欢迎访问三七文档
超弦理論によるQCDの解析KEK研究会「ハドロン物理と超弦理論の再会」@KEK2007/3/5-7杉本茂樹(名大理)hep-th/0412141hep-th/0507073basedon:T.SakaiandS.S.①IntroductionClaim4dim(largeN)QCDtheoryofmesonslowenergy5dimgaugetheoryinacurvedbackgroundgauge/gravitydualityHowcanitbepossible?4dim5dim5dimtheory4dimtheorywith∞particlescf)compactification5dim4dim(:fixed)★largeNQCDConsider4dimQCDwith.Inthelimit,expansionworks(atleastqualitatively)evenfortherealisticQCD.thereareinfinitelymanystablemesons.5dimdescriptioncouldbeagoodapproximationtorealisticQCD.gluonquarkcolorflavor[’tHooft1974]Howcanwefindit?1.ConstructQCDusingD-branesinstringtheory2.Useconjecturedgauge/gravityduality★gauge/gravitydualityConjectureparticleSolutionofEinsteineq.cf)D-braneSupergravitysolutionduallargeN,largeλSUGRAapproximationGaugetheoryStringtheoryinthecurvedb.g.ex)AdS/CFTcorrespondence[Maldacena1997]Imamura’stalkWhatisnice?Wecanuse*knowledgeofQCD*experimentaldatatotesttheconjecturedgauge/gravityduality.(non-trivialtestsfornon-SUSY,non-CFTversion)AnewwaytoanalyzeQCD.→applicationtophenomenologyQCDisoneofourfavoriteQFT.Anyway,itisfun!OutlineStringtheoryQCDSupergravityHadronphysicsD4/D8system5dimYM-CStheoryPlanofTalk①Introduction②ConstructionofQCD③Exploration④Summaryanddiscussion②ConstructionofQCD★buildingblocksYang-MillsquarksQCD=YM+quarksAddprobeD8-branes.[Kruczenski-Mateos-Myers-Winter2003]cf)KMMWmodel:D4+probeD6D4-braneonwith[Witten1998]CorrespondingSUGRAsolutionisknown.SUSYfermionImamura’stalk★thebraneconfiguration[cf)S.S.-K.Takahashi2004]4dimQCDwithmasslessquarks※addingmassHashimoto’stalkD4WeassumeOnlyD4-braneisreplacedwiththeSUGRAsolution.pairsaretreatedasprobes.heavylightprobecf)★ProbeapproximationD8[Karch-Katz2002](difficulttomakelarge)★Howrealisticour“QCD”is?Ouranalysisisreliablewhen:largelargescaleof5thdimension(probeapproximation)Weshouldnotbetooseriousinthequantitativecomparisonwiththeexperiments.But,believeitornot,theagreementisquiteimpressive.③ExplorationChiralsymmetrybreakingUnificationofmesonsmass&couplingsVectormesondominanceWZWtermGSWmodelhighlights★ChiralsymmetrybreakingandmustbeconnectedintheD4background.WereplaceD4withtheSUGRAsol.interpretedasthechiralsymmetrybreaking!connected★Wherearemesons?closedstringopenstringglueballsmesonsreducedto5dimgaugetheoryTheeffectivetheoryisa9dimgaugetheoryThereisansymmetry(mesonsinrealisticQCDliveinthissector)※Today,weonlyconsiderthesingletstates,forsimplicity.Note:(studiedaround1998)Imamura’stalkD8-braneactionD4chargeCS5-formInsertingtheSUGRAsolution,This5dimYM-CStheoryisconsideredastheeffectivetheoryofmesons.[cf)Son-Stephanov2003]Tachibana’stalkChosentodiagonalizeKinetic&masstermsof★modeexpansioncompletesetsUsingthese,weobtaineatenmasslessscalarmesonmassivevectormesonareunifiedinthe5dimgaugefield!Weinterpret★andmassspectrumWecanshowconsistentwithourinterpretationinputnotestablished(axial-)vectormesonmassResidualgaugesymmetryconstants.t.WehaveimplicitlyassumedThisisinterpretedasIfyouwantto‘gauge’thechiralsymmetry,thecorrespondinggaugefieldsappearas★chiralsymmetryinterpretedasthepionfieldtransformsasDefineItisalsousefultodefinetransformsas“hidden”localsymmetry[Bando-Kugo-Uehara-Yamawaki-Yanagida1985](highermodesaregaugedaway.)(appropriatelychosen)★TwousefulgaugechoicesTheinteractionbetweenandisgreatlysimplifiedwhenwetakethelimit.①gaugebythegaugetr.withWecanmovetogaugePionappearsintheboundaryconditionThemodeexp.consistentwiththisb.c.is※Itisoftenusefultotake.manifestchiralsymmetry,HLS②gauge★effectiveactioningauge(DBIpart)ThisistheSkyrmemodelaction.Insertingthemodeexpansionintothe5dimaction,weobtainIfwefixtofit,weobtainNote:Kojo’stalk★effectiveactioningauge(DBIpart):fieldstrengthofisdivergentisaglobalsymmetrycoupleonlythroughtheaboveterms.★KSRFrelationWorkinginthegauge,the3ptcouplingiscalculatedas.(ourmodel)(experiment)[Kawarabayashi-Suzuki1966][Riazuddin-Fayyazddin1966](KSRF)Note:[cf)DaRold-Pomarol2005]★includingphotonele-maggaugefieldisintroducedbysettingchargematrixWeobtainwithNote:[cf)Son-Stephanov2003](ourmodel)(experiment)pionformfactoriscomputedas★pionformfactor“vectormesondominance”chargeradiusIfwefixbyfittingthemesonmass,weobtain(ourmodel)(experiment)[Gell-Mann-Zachariasen1961][Sakurai1969]★WZWtermreproducesthewell-knownformula.Usingthegauge,weobtainWZWtermisobtainedbysimplyinsertingthemodeexpansionintotheCS-term.★includingvectormesonsinWZWtermWorkinginthegauge,weobtainwithMoreover,onecanshowAllthetermsincludingarecancelled.(completevectormesondominance)Termswithmorethanonepionfieldvanish.★andTherelevantdiagramsforthesedecayareExactlythesameastheGSWmodel![Gell-Mann-Sharp-Wagner1962]Furthermore,wefindreproducestheproposalgivenbyFujiwaraetal![Fujiwara-Kugo-Terao-Uehara-Yamawaki1985]★OthertopicsaxialanomalyBaryonasinstantonSakai’stalk(SeealsoKojo’stalk)mesonmass(Witten-Venezianoformula)★Furtherdevelopmentcorrection(pionloop)[Harada-Matsuzaki-Yamawaki2006]Finitetemperature[Aharony-Sonnenschein-Yankielowicz,Parnachev-Sahakyan,Peeters-Sonnenschein-Zamaklar2006]Viscosityinhightemperaturepha
本文标题:超弦理论 による.
链接地址:https://www.777doc.com/doc-3859643 .html