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String Theory In Nutshell.pdf

String Theory In Nutshell.pdf

上传者: oztron 2012-07-25 评分 0 0 0 0 0 0 暂无简介 简介 举报

简介:本文档为《String Theory In Nutshellpdf》,可适用于工程科技领域,主题内容包含BookreviewStringTheoryinaNutshellEliasKiritsisPrinceton,NJ:PrincetonUniver符等。

BookreviewStringTheoryinaNutshellEliasKiritsisPrinceton,NJ:PrincetonUniversityPresspp,UK,US$ISBN:Thebook‘StringTheoryinaNutshell’byEliasKiritsisprovidesacomprehensiveintroductiontomodernstringtheoryStringtheoryistheleadingcandidateforatheorythatsuccessfullyunifiesallfundamentalforcesofnature,includinggravityThesubjecthasbeencontinuouslydevelopingsincetheearlys,withclassictextbooksonthesubjectbeingthoseofGreen,SchwarzandWitten()andPolchinski()Sincethelatterwaspublishedtherehavebeensubstantialdevelopments,inparticularinunderstandingblackholesandgravitygaugetheorydualitiesAtextbooktreatmentofthisimportantmaterialisclearlyneeded,bothbystudentsandresearchersinstringtheoryandbymathematiciansandphysicistsworkinginrelatedfieldsThisbookhasagoodselectionofmaterial,startingfrombasicsandmovingintoclassicandmoderntopicsInparticular,Kiritsis’presentationofthebasicmaterialiscomplementarytothatoftheearliertextbooksandheincludesanumberoftopicswhicharenoteasilyfoundorcoveredadequatelyelsewhere,forexample,loopcorrectionstostringeffectivecouplingsOverallthebooknicelycoversthemajoradvancesofthelasttenyears,including(nonperturbative)stringdualities,blackholephysics,AdSCFTandmatrixmodelsItprovidesaconcisebutfairlycompleteintroductiontothesesubjectswhichcanbeusedbothbystudentsandbyresearchersMoreovertheemphasisisonresultsthatarereasonablyestablished,asisappropriateforatextbookconcisesummariesaregivenforsubjectswhicharestillinflux,withreferencestorelevantreviewsandpapersApositivefeatureofthebookisthatthebibliographysectionsattheendofeachchapterprovideacomprehensiveguidetotheliteratureThebibliographiespointtoreviewsandpedagogicalpapersonsubjectscoveredinthisbookaswellasthosethatwereomittedItisrareforatextbooktocontainsuchaselfcontainedanddetailedguidetotheliteratureInall,thebookcontainsnearlyfivehundredexercisesforthegraduatelevelstudent,whichareusefulbothinteachingcoursesonstringtheoryandforthosewhoarestudyingbythemselvesAnicefeatureofthisbookisthatreferencesaremadetospecificpagesearlierinthebook,ratherthantochapters,whichishelpfulforstudentsworkingthroughthebookontheirownInsummary,‘StringTheoryinaNutshell’isavaluableadditiontotheexistingstringtheorytextbooksitiscomplementarytothepreviousbooksandgivesagoodtreatmentofsubsequentdevelopmentsItislikelytobecomeastaplereferenceonthesubject,usedbothbystudentsandresearchersKostasSkenderisInstituteofTheoreticalPhysics,UniversiteitvanAmsterdam,Valckenierstraat,NLXEAmsterdam,TheNetherlandsContentsPrefacexvAbbreviationsxviiIntroductionPrehistoryTheCaseforStringTheoryAStringyHistoricalPerspectiveConventionsBibliographyClassicalStringTheoryThePointParticleRelativisticStringsOscillatorExpansionsClosedstringsOpenstringsTheVirasoroconstraintsBibliographyExercisesQuantizationofBosonicStringsCovariantCanonicalQuantizationLightconeQuantizationSpectrumoftheBosonicStringUnorientedStringsOpenstringsandChanPatonfactorsPathIntegralQuantizationIntroductionPrehistoryThequestinphysicshasbeenhistoricallydominatedbyunravelingthesimplicityofthephysicallaws,movingmoreandmoretowardtheelementaryAlthoughthisisnotguaranteedtosucceedindefinitely,ithasbeenvindicatedsofarTheotherorganizingtendencyofthehumanmindistoward“unification”:findingauniqueframeworkfordescribingseeminglydisparatephenomenaThephysicsofthelatenineteenthandtwentiethcenturiesisaseriesofdiscoveriesandunificationsMaxwellunifiedelectricityandmagnetismEinsteindevelopedthegeneraltheoryofrelativitythatunifiedtheprincipleofrelativityandgravityInthelates,therewasaculminationoftwodecades’effortsintheunificationofelectromagnetismandquantummechanicsInthesands,thetheoryofweakandelectromagneticinteractionswasalsounifiedMoreover,aroundthesameperiodtherewasalsoawiderconceptualunificationThreeofthefourfundamentalforcesknownweredescribedbygaugetheoriesThefourth,gravity,isalsobasedonalocalinvariance,albeitofadifferenttype,andsofarstandsapartThecombinedtheory,containingthequantumfieldtheoriesoftheelectroweakandstronginteractionstogetherwiththeclassicaltheoryofgravity,formedtheStandardModeloffundamentalinteractionsItisbasedonthegaugegroupSU()SU()U()ItsspingaugebosonsmediatethestrongandelectroweakinteractionsThematterparticlesarequarksandleptonsofspininthreecopies(knownasgenerationsanddifferingwidelyinmass),andaspinparticle,theHiggsboson,stillexperimentallyelusive,thatisresponsibleforthespontaneousbreakingoftheelectroweakgaugesymmetryToday,wehavesomeintriguingevidencethatevengravitymaybeastrongcouplingfacetofanextraunderlyingfourdimensionalgaugetheory|ChapterTheStandardModelhasbeenexperimentallytestedandhassurvivedthirtyyearsofacceleratorexperimentsThishighlysuccessfultheory,however,isnotsatisfactory:•Aclassicaltheory,namely,gravity,describedbygeneralrelativity,mustbeaddedtotheStandardModelinordertoagreewithexperimentaldataThistheoryisnotrenormalizableatthequantumlevelInotherwords,newinputisneededinordertounderstanditshighenergybehaviorThishasbeenachallengetothephysicscommunitysincethesand(apartfromstringtheory)verylittlehasbeenlearnedonthissubjectsincethen•ThethreeSMinteractionsarenotcompletelyunifiedThegaugegroupissemisimpleGravityseemsevenfurtherfromunificationwiththegaugetheoriesArelatedproblemisthattheStandardModelcontainsmanyparametersthatlookaprioriarbitrary•Themodelisunstableasweincreasetheenergy(hierarchyproblemofmassscales)andthetheorylosespredictivityasonestartsmovingfarfromcurrentacceleratorenergiesandclosertothePlanckscaleGaugebosonsareprotectedfromdestabilizingcorrectionsbecauseofgaugeinvarianceThefermionsareequallyprotectedduetochiralsymmetriesTherealculpritistheHiggsbosonSeveralattemptshavebeenmadetoimproveontheproblemsaboveThefirstattemptsfocusedonimprovingonunificationTheygaverisetothegrandunifiedtheories(GUTs)AllinteractionswerecollectedinasimplegroupSU()inthebeginning,butalsoSO(),E,andothersThefermionsofagivengenerationwereorganizedinthe(larger)representationsoftheGUTgroupThereweresuccessesinthisendeavor,includingthepredictionofsinθWandthepredictionoflightrighthandedneutrinosinsomeGUTsHowever,therewasaneedforHiggsbosonstobreaktheGUTsymmetrytotheSMgroupandthehierarchyproblemtookitstollbymakingittechnicallyimpossibletoengineeralightelectroweakHiggsThephysicscommunityrealizedthatthefocusmustbeonbypassingthehierarchyproblemAfirstideaattackedtheproblematitsroot:itattemptedtobanishtheHiggsbosonasanelementarystateandtoreplaceitwithextrafermionicdegreesoffreedomItintroducedanewgaugeinteraction(termedtechnicolor)whichboundsthesefermionsstronglyoneofthetechnihadronsshouldhavetherightpropertiestoreplacetheelementaryHiggsbosonasresponsiblefortheelectroweaksymmetrybreakingThenegativesideofthislineofthoughtisthatitreliedonthenonperturbativephysicsofthetechnicolorinteractionRealisticmodelbuildingturnedouttobedifficultandeventuallythislineofthoughtwasmostlyabandonedAcompetingideareliedonanewtypeofsymmetry,supersymmetry,thatconnectsbosonstofermionsThispropertyturnedouttobeessentialsinceitcouldforcethebadmanneredspinbosonstobehaveaswellastheirspinpartnersThisworkswell,butsupersymmetrystipulatedthateachSMfermionmusthaveaspinsuperpartnerwithequalmassThisbeingobviouslyfalse,supersymmetrymustbespontaneouslybrokenatWiththeexceptionoftheneutrinosectorthatwassuspectedtobeincompleteandiscurrentlythesourceofinterestingdiscoveriesIntroduction|anenergyscalenotfarawayfromtoday’sacceleratorenergiesFurtheranalysisindicatedthatthebreakingofglobalsupersymmetryproducedsuperpartnerswhosemasseswerecorrelatedwiththoseofthealreadyknownparticles,inconflictwithexperimentaldataToavoidsuchconstraintsglobalsupersymmetryneededtobepromotedtoalocalsymmetryAsasupersymmetrytransformationisinasensethesquarerootofatranslation,thisentailedthatatheoryoflocalsupersymmetrymustalsoincorporategravityThistheorywasfirstconstructedinthelates,andwasfurthergeneralizedtomakemodelbuildingpossibleTheflipsideofthiswasthattheinclusionofgravityopenedthePandora’sboxofnonrenormalizabilityofthetheoryHopesthat(extended)supergravitymightberenormalizablesoonvanishedInparallelwiththedevelopmentsabove,apartofthecommunityresurrectedtheoldideaofKaluzaandKleinofunifyinggravitywiththeothergaugeinteractionsIfonestartsfromahigherdimensionaltheoryofgravityandcompactifiesthetheorytofourdimensions,oneendswithfourdimensionalgravityplusextragaugeinteractionsAlthoughgravityinhigherdimensionsismoresingularintheUV,physicistshopedthatatleastattheclassicallevelonewouldgetatheorythatisveryclosetotheStandardModelAlthoughprogresswasmade,astumblingblockturnedouttobeobtainingafourdimensionalchiralspectrumoffermionsasintheSMAlthoughnoneofthedirectionsaboveprovidedafinalandsuccessfultheory,theingredientswereveryinterestingideasthatmanyfeltwouldformapartoftheultimatetheoryTheCaseforStringTheoryStringtheoryhasbeentheleadingcandidateoverthepasttwodecadesforatheorythatconsistentlyunifiesallfundamentalforcesofnature,includinggravityItgainedpopularitybecauseitprovidesatheorythatisUVfiniteThebasiccharacteristicofthetheoryisthatitselementaryconstituentsareextendedstringsratherthanpointlikeparticlesasinquantumfieldtheoryThismakesthetheorymuchmorecomplicatedthanQFT,butatthesametimeitimpartssomeuniquepropertiesOneofthekeyingredientsofstringtheoryisthatitprovidesafinitetheoryofquantumgravity,atleastinperturbationtheoryToappreciatethedifficultieswiththequantizationofEinsteingravity,welookatasinglegravitonexchangebetweentwoparticles(Figa))Then,theamplitudeisproportionaltoEMP,whereEistheenergyoftheprocessandMPisthePlanckmass,MPGeVItisrelatedtotheNewtonconstantasMP=()πGNAlthoughthereisnorigorousprooftoallordersthatthetheoryisUVfinite,thereareseveralallordersargumentsaswellasrigorousresultsatlowlooporderInclosedstringtheory,amplitudesmustbecarefullydefinedviaanalyticcontinuation,standardinSmatrixtheoryWhenopenstringsarepresent,therearedivergencesHowever,theyareinterpretedasIRdivergences(duetotheexchangeofmasslessstates)inthedualclosedstringchannelTheyaresubtractedinthe“Wilsonian”Smatrixelements|Chaptera)b)FigureGravitationalinteractionbetweentwoparticlesviagravitonexchangeTherefore,thegravitationalinteractionisirrelevantintheIR(EMP)butstronglyrelevantintheUVInparticular,thisimpliesthatthetwogravitonexchangediagram(Figb))isproportionaltothedimensionlessratioEEdEE,()MPMPwhereEistheoutgoingparticleenergyandEistheinternalparticleenergyThisisstronglyUVdivergentItisknownthatEinsteingravitycoupledtomatterisnonrenormalizableinperturbationtheorySupersymmetrymakestheUVdivergencesofterbutthenonrenormalizabilitypersistsTherearetwowaysoutofthis:•ThereisanontrivialUVfixedpointthatgovernsthehighenergybehaviorofquantumgravityTodate,nocredibleexampleofthispossibilityhasbeenoffered•ThereisnewphysicsatEMP(orevenlower)andEinsteingravityistheIRlimitofamoregeneraltheory,validatandbeyondthePlanckscaleYoucouldconsidertheanalogoussituationwiththeFermitheoryofweakinteractionsThere,anonrenormalizablecurrentcurrentinteractionwithsimilarproblemsoccurred,buttodayweknowthatthisistheIRlimitofthestandardweakinteractionmediatedbytheWandZgaugebosonsSofar,thereisnoconsistentfieldtheorythatcanmakesenseatenergiesbeyondMPandcontainsgravityGoodreviewsoftheultravioletproblemsofEinsteingravitycanbefoundin,StringsprovideatheorythatinducesnewphysicsatthestringscaleMswhichinperturbationtheory(thestringcouplinggsbeingweak)ismuchlowerthanthePlanckscaleMPItisstilltrue,however,thatthestringperturbationtheorybecomesuncontrollablewhentheenergiesapproachthePlanckscaleTherearetwoimportantreasonswhyclosedstringtheorydoesnothaveUVdivergencesOneisthefactthatstringdynamicsandinteractionsareinextricablylinkedtothegeometryoftwodimensionalsurfacesForexample,forclosedstrings,bydecomposingthestringIntroduction|FigureOpenandclosedRiemannsurfacesFeynmandiagrams,itisobviousthatthereisessentiallyauniversalthreepointinteractioninthetheoryThisinteractionisdictatedbythetwodimensionalgeometryofclosedRiemannsurfacesasisobviousfromfigureTheotherrelatedreasonisthepresenceofaninfinitetowerofexcitationswithmassesinmultiplesofthestringscaleTheirinteractionsarecarefullytunedtobecomesoftatdistanceslargerthanthestringlengthsbutstilllongerthanthePlancklengthPForopenstringsthesituationissubtlerThere,UVdivergencesarepresent,butareinterpretedasIRclosedstringdivergencesinthedualclosedstringchannelThisUVIRopenclosedstringdualityisattheheartofmanyoftherecentdevelopmentsinthefieldAnotherkeyingredientofstringtheoryisthatitunifiesgravitywithgaugeinteractionsItdoesthisinseveraldifferentwaysThesimplestisviathetraditionalKKapproachSuperstringtheorytypicallyisdefinedintendimensionsStandardfourdimensionalvacuacanbeobtainedviacompactificationonasixdimensionalcompactmanifoldHowever,gaugesymmetrycanalsoarisefromDbranesthatsometimesarepartofthevacuum(asinorientifolds)ThereisevengaugesymmetrycomingfromanongeometricalpartofthetheoryashappensintheheteroticstringTheunifiedoriginofgravityandgaugesymmetryextendsevenfurthertootherinteractionsForexample,theYukawainteractions,crucialforgivingmasstotheSMparticles,arealsointimatelyrelatedtothegaugeinteractionsUnlikeearlierKaluzaKleinapproachestounification,stringtheoryiscapableofproviding,uponappropriatecompactifications,chiralmatterinfourdimensionsThishappensviaasubtleinterplaybetweenanomalyrelatedinteractionsandtheprocessofcompactificationAnothercharacteristicingredientofstringtheoryisthatthepresenceofspacetimefermionsinthetheoryimpliestheappearanceofspacetimesupersymmetryatleastathighenergiesSupersymmetry,consequently,isanimportantingredientofthetheoryTherearegoodreasonstobelievethatthetheoryisunique,althoughtherearemanypossiblevacuathatcouldbestableRecentunderstandingofnonperturbativedualitieshasstrengthenedthebeliefintheuniquenessofthisstringtheorystructureIthasalsopointedoutnewcornersintheoveralltheory,whichmanycallMtheory,thatarestillunchartedDespiteallthis,stringtheory,afterthirtyfiveyearsofresearch,hasmanyimportantquestionsstillunansweredPhysicistsfeelthatthefundamentaldefinitionofthetheoryisnotknownHowitfitstherealworldindetailisalsonotknownpresently|ChapterItmaybethatstringtheorywillturnintoan“intellectualclassicalblackhole”ItmayalsobethatitisthecorrectdescriptionofphysicsatshortdistancesTimeandexperimentwillshowAStringyHistoricalPerspectiveInthes,physiciststriedtomakesenseofalargeamountofexperimentaldatarelevanttothestronginteractionTherewerelotsofparticles(or“resonances”)andthesituationcouldbestbedescribedaschaoticSomeregularitieswereobserved:AlmostlinearReggebehaviorItwasnoticedthatarelativelylargenumberofresonancescouldbenicelyputon(almost)straightlinesbyplottingtheirmassversustheirspinJm=α,()α′withα′GeVthisrelationwascheckeduptoJ=stdualityIfweconsiderascatteringamplitudeoftwohadronstwohadrons(,,),thenitcanbedescribedbytheMandelstaminvariantss=(pp),t=(pp),u=(pp),()withstu=imiWeareusingametricwithsignature()Suchanamplitudedependsontheflavorquantumnumbersofhadrons(forexampleSU())Considertheflavorpart,whichiscyclicallysymmetricinflavorspaceForthefullamplitudetobesymmetric,itmustalsobecyclicallysymmetricinthemomentapiThissymmetryamountstotheinterchangetsThus,theamplitudeshouldsatisfyA(s,t)=A(t,s)ConsideratchannelcontributionduetotheexchangeofaspinJparticleofmassMThen,athighenergy(s)JAJ(s,t)()tMThus,thispartialamplitudeincreaseswithsanditsbehaviorbecomesworseforlargevaluesofJIfonesewsamplitudesofthisformtogethertomakealoopamplitude,thenthereareuncontrollableUVdivergencesforJ>Anyfinitesumofamplitudesoftheform()hasthisbadUVbehaviorMoreover,suchafinitesumhasnoschannelpolesHowever,ifoneallowsaninfinitenumberoftermsthenitisconceivablethattheUVbehaviormightbedifferentAproposalforsuchadualamplitudewasmadebyVeneziano,(α(s))(α(t))A(s,t)=,()(α(s)α(t))whereisthestandardEulerfunctionandα(s)=α()α′s()Introduction|Byusingthestandardpropertiesofthefunction,itcanbecheckedthattheamplitude()hasaninfinitenumberofs,tchannelpoles:(α(s))(α(s)n)A(s,t)=()n!α(t)nn=Inthisexpansion,thestinterchangesymmetryof()isnotmanifestThepolesin()correspondtotheexchangeofaninfinitenumberofparticlesofmassM=(nαα′())andhighspinsItcanalsobecheckedthatthehighenergybehavioroftheVenezianoamplitudeissofterthananylocalquantumfieldtheoryamplitude,andtheinfinitenumberofpolesiscrucialforthisItwassubsequentlyrealizedbyNambu,Goto,Nielsen,andSusskindthatsuchamplitudescameoutoftheoriesofrelativisticstringsHo

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