关闭

关闭

封号提示

内容

首页 1101.0336v4.pdf

1101.0336v4.pdf

1101.0336v4.pdf

上传者: 最迷仙 2013-09-23 评分1 评论0 下载8 收藏0 阅读量133 暂无简介 简介 举报

简介:本文档为《1101.0336v4pdf》,可适用于剑侠世界领域,主题内容包含arXiv:vhepthJulBulkMatterFieldsonTwofieldThickBranesChunEFu,YuXiaoLiu†,Hen符等。

arXiv:vhepthJulBulkMatterFieldsonTwofieldThickBranesChunEFu,YuXiaoLiu†,HengGuo‡InstituteofTheoreticalPhysics,LanzhouUniversity,Lanzhou,People’sRepublicofChinaAbstractInthispaperweobtainanewsolutionofabranemadeupofascalarfieldcoupledtoadilatonThereisauniqueparameterbinthesolution,whichdecidesthedistributionoftheenergydensityandwilleffectthelocalizationofbulkmatterfieldsForfreevectorfields,wefindthatthezeromodecanbelocalizedonthebraneAndforvectorfieldscoupledwiththedilatonviaeτpiFMNFMN,theconditionforlocalizingthezeromodeisτbwith<b,orτ>bwithb>,whichincludesthecaseτ=WhilethezeromodeforfreeKalbRamondfieldscannotbelocalizedonthebrane,ifonlyweintroduceacouplingbetweentheKalbRamondfieldsandthedilatonviaeζpiHMNLHMNLWhenthecouplingconstantsatisfiesζ>bwithborζ>bbwith<b<,thezeromodefortheKRfieldscanbelocalizedonthebraneForspinhalffermionfields,weconsiderthecouplingηΨeλpiφΨbetweenthefermionsandthebackgroundscalarswithpositiveYukawacouplingηTheeffectivepotentialsforbothchiralfermionshavethreetypesofshapesdecidedbytherelationbetweenthedilatonfermioncouplingconstantλandtheparameterbForλb,thezeromodeofleftchiralfermioncanbelocalizedonthebraneWhileforλ>bwithb>orb<λ<bwith<b,thezeromodeforleftchiralfermionalsocanbelocalizedPACSnumbers:h,dfuchelzucn†liuyxlzueducn,correspondingauthor‡guohlzucnIINTRODUCTIONThebranetheory,,whichconsidersourfourdimensionaluniverseasahypersurface(“braneworld”)embeddedinmorehigherdimensionalspacetime,hasreceivedagreatofrenewedattentionInthistheoryallmatterfieldsareconfinedtothebraneinahighdimensionalspace,whileonlygravityisfreetopropagateinalldimensionsTheextradimensionscanbecompact–,orinfiniteandnoncompact,Thistheoryhasopenedupnewavenuestoexplainsomequestionsinparticlephysicsandinastrophysics,suchasthehierarchyproblem,thecosmologicalproblem,thenatureofdarkmatteranddarkenergy–,–Somebranemodelsconsiderthebraneasinfinitelythinbraneswithdeltalikelocalizationofmatter,whichareidealmodels–SosomethickbranemodelsareproposedThethickbranesareusuallyrealizednaturallybyone–ortwo–backgroundscalarfieldsconfigurationcoupledwithgravityForacomprehensivereviewonthickbranesolutionsandrelatedtopicspleaseseeRefInthispaper,wewillinvestigatethelocalizationofvariousmatterfieldsonathickbranegeneralizedbytwobackgroundscalarfields,ie,akinkscalarandadilatonscalar,whichissimilartothatinRefs,Butinoursolutionofthebranethereisauniqueparameterb,whichmakesthesolutioninRefs,onlyonecaseofusTheuniqueparameterbdecidesthedistributionoftheenergydensityofthebulk,andwilleffectthelocalizationofvariousbulkmatterfieldsdifferentlyThelocalizationofvariousmatterfieldsonthebranesisanimportantprobleminthebraneworldtheory,whichinordertobuildupthestandardmodelIthasbeenknownthatmasslessscalarfieldsandgravitoncanbelocalizedonbranesofdifferenttypes,,withexponentiallydecreasingwarpfactorButspinAbelianvectorfieldsonlycanbelocalizedontheRSbraneinsomehigherdimensionalcases,oronthethickdeSitterbraneandtheWeylthickbrane,TheantisymmetricKalbRamond(KR)tensorfieldBµνwasfirstintroducedinthestringtheory,inwhichitisassociatedwithmasslessmodesThenitwasusedtoexplainthetorsionofthespacetimeintheEinsteinCartantheoryMoreoverinthefourdimensionalspacetime,byasymmetryknownasduality,antisymmetrictensorfieldsarejustequivalenttoscalarorvectorfieldsButinextradimensionstheywillindicatenewtypesofparticlesThusanyobservationaleffectinvolvingtheKRfieldsisawindowintotheinaccessibleworldofveryhighenergyphysicsTheinvestigationoftheKRfieldsinthecontextoftheorieswithextradimensionshasbeencarriedoutinRefs,–InRefs–,theauthorsprovedthatinthebackgroundofRSspacetimeboththemasslessandthemassiveKKmodesoftheKRfieldsappearmuchweakerthancurvaturetoanobserveronthevisibleRSbrane,howeverwhentheKRfieldscouplewiththedilatonfields,thetrilineardilatonKRcouplingsmayleadtonewsignalsinTevscaleexperimentsWhileinRef,theauthoralsoprovedthatonlywhentheKRfieldscouplewiththedilaonfield,thezeromodeoftheKRfieldscanbelocalizedonathickbraneButthereisonlyazeromodeandnoboundmassiveKKmodeInourworkwealsofindthatitisnecessarytointroducethedilatonKRcouplinginordertoobtainalocalizedzeromode,andwefindtherearemassiveboundKKmodesAndthelocalizationofthespinfermionfieldsisalsointerestingIthasbeenprovedthatinordertohavenormalizablezeromodesthefermionfieldsshouldcouplewiththebackgroundscalarsWithdifferentscalarfermioncoupling,theremayexistasingleboundstateandacontinuousgaplessspectrumofmassivefermionKKstates,–,orexistfinitediscreteKKstates(massgap)andacontinuousgaplessspectrumstartingatapositivem,–,orevenonlyexistboundKKmodes,Whileinthispaper,wewillshowthatwithonescalarfermioncouplingtobothbackgroundscalars,therewillexisttheabovethreecaseswithdifferentrelationbetweentheuniqueparameterbandthedilatonfermioncouplingconstantOurpaperisorganizedasfollows:InSecII,wegiveabriefreviewofthebraneworldgeneratedbytwoscalarsThen,inSecIII,westudythelocalizationandmassspectraofthevector,KR,andfermionfieldsonthebranebypresentingthepotentialsofthecorrespondingSchrodingerequationsFinally,abriefdiscussionandconclusionaregiveninthelastsectionIIREVIEWOFTHEBRANEGENERATEDBYTWOINTERACTINGSCALARSInthispaperweconsiderthebraneworldgeneratedbytwointeractingscalarsφandpiTheactionofthesystemisS=dxgκR(φ)(pi)V(φ,pi)()withRthescalarcurvatureandκ=piG,whereGisthedimensionalNewtonconstantHerewesetκ=Thelineelementofadimensionalspacetimecanbeassumedas,,ds=eA(y)ηµνdxµdxνeB(y)dy,()whereeAandeBarethewarpfactorsandystandsfortheextracoordinateAndthebackgroundscalarsφ,piareassumedtobeonlythefunctionsofy,becausethebranecanbetreatedasthecrosssectionofthebulkInthismodel,thethickbraneisrealizedbythepotentialV(φ,pi)Thentheequationsofmotiongeneratedfromtheaction()withtheansatz()aregivenbyφ′pi′eBV=A′,()φ′pi′eBV=A′A′′A′B′,()φ′′(A′B′)φ′=eBVφ,()pi′′(A′B′)pi′=eBVpi,()wheretheprimestandsforthederivativewithrespecttoyThesolutionsofthesystemcanbefoundbyfollowingthesuperpotentialmethodWiththesuperpotentialfunctionW(φ)andsupposeV=ebpi(Wφ)bW,itcanbeverifiedthatthefollowingfirstorderdifferentialequationsarethesolutionsoftheequationsofmotion():φ′=Wφ,A′=W,B=bA,pi=bA,()wherebisapositiveconstantForaspecificsuperpotentialW(φ),:W(φ)=vaφ(φv),()thesolutionsarefoundtobeφ(y)=vtanh(ay),()A(y)=v(lncosh(ay)tanh(ay)),()pi(y)=bA(y),()B(y)=bA(y),()wherev,aarebothpositiveconstantsItcanbeseenthatthesolutionforφisakinkandpi=bAisthedilatonfieldconsistentwiththemetricandthekinkThesolutionsinRefs,areonlyonecaseofabovesolutionswhenweletv=βandb=Andherewehaveanotherparameterb,whichleadstonewsolutionsofthebraneworldOursolutionsforthebranearenotamounttoasimplecoordinatechange,becausethesolutionsaredecidedbythescalarpotentialV(φ)withtheparameterb,whichdoesnotdependonthecoordinatesystemsInordertoclarifythisquestionmoreclearly,wewouldliketodiscusstheeffectoftheparameterbonthebraneunderthephysicalcoordinateyTothisend,weperformacoordinatetransformationdy=ebAdytotranslatethedifferentcoordinateytothesamephysicalcoordinateyThenthemetricisreadasds=eA(y(y))ηµνdxµdxνdy()Withtherelationofthetwocoordinatesystemswehavey=yebAdyyevabydy,fory,()soitcanbeseenthatinthisnewcoordinatesystemtheextradimensionyisfinite(withymax=vab),whichisdifferentfromtheunphysicalandinfinitecoordinateyFordifferentb,theboundaryoftheextradimensionyisalsodifferentNowwecaninvestigatetheenergydensityofthesystemT(y)inthenewcoordinateWiththesolution()andtherelationbetweenthetwocoordinateswecalculatethevaluesoftheenergydensityT(y)aty=andat|y|ymax:T()=av,()T(|y|ymax)av(b)(vaby)(b)b,()fromwhichwecanseethatthebehaviorofT(|y|ymax)attheboundariesoftheextradimensionis:T(|y|ymax)=,<b<av,b=,<b<,b=,b>(a)yTHb=LyTHb=LyTHb=LTHb=LyTHb=LFIG:TheshapesoftheenergydensityT(y)fordifferentbTheparametersaresettoa=,v=WeplottheenergydensityT(y)fordifferentbusingnumericalmethodinFigInthefollowingwewillmainlydiscusstheeffectoftheparameterbonthelocalizationofbulkmatterfieldsIIILOCALIZATIONANDMASSSPECTRAOFVARIOUSBULKMATTERFIELDSONTHEBRANEInthissectionwewillinvestigatethelocalizationandmassspectraofvariousbulkmatterfieldsinthisbraneworldbypresentingthepotentialsofthecorrespondingSchrodingerequationsInordertomakesurethesolutionsofthesystemobtainedbeforevalid,wetreatthebulkmatterfieldsconsideredbelowasperturbationsaroundthebackground,,namely,weneglectthebackreactionofbulkmatterfieldsonthebackgroundgeometryAndwewillusetheconformallyflatmetricds=eA(z)(ηµνdxµdxνdz)()Comparingitwiththemetric(),wefindthetwocoordinatesystemsareconnectedbydz=e(b)AdyFortheconformallyflatspacetime,theextradimensionzwillbeinfinitefor<bandfinite(with|z|zmax=va(b))forb>Fromthefollowingcalculationswecanseethatthemassindependentpotentialscanbeobtainedconvenientlywiththeconformallyflatmetric(),andwewillmainlyinvestigatetheeffectoftheparameterbonthezeromodesandthespectraforvariousbulkmatterfieldsASpinvectorfieldsFirstweinvestigatethelocalizationofthespinvectorfieldsindimensionalspaceTheactionofvectorfieldscoupledwiththedilatonisS=dxgeτpigMRgNSFMNFRS,()wherethefieldstrengthtensorisgivenbyFMN=MANNAMandτisthecouplingconstantbetweenthedilatonandthevectorfieldTheequationsofmotioncanbeobtainedusingthebackgroundgeometry():eτpigˆν(gˆgˆνρgˆµλFρλ)gˆµλeA(e(Aτpi)Fλ)=,()eτpiµ(gˆgˆµνFν)=()ThenwiththegaugechoiceA=andthedecompositionofthevectorfieldAµ(x,z)=na(n)µ(x)ρn(z)e(bτ)A,wefindthattheKKmodesofthevectorfieldsatisfythefollowingSchrodingerlikeequation:zV(z)ρn(z)=mnρn(z),()withmnthemassesofthedimensionalvectors,andtheeffectivepotentialisV(z)=(bτ)(zA)bτzA()Furthermore,providingtheorthonormalityconditionzbzbdzρm(z)ρn(z)=δmn,()wecangetthedimensionaleffectiveaction:S=ndxgˆ(gˆµαgˆνβf(n)µνf(n)αβmngˆµνa(n)µa(n)ν),()wheref(n)µν=µa(n)ννa(n)µisthedimensionalfieldstrengthtensorWerewritethepotential()asthefunctionofy:V(y)=e(b)AbτyA(bτ)(bτ)(b)(yA)()Sowiththerelationdz=e(b)Ady,wecangetthevaluesofV(z)atz=and|z|zb:V()=av(bτ),()V(|z|zb)=va(bτ)(bbτ)va(b)z()Inordertogetazeromode,wehavetoinsurethatthevalueofV(z)atz=isnegative,theconditionisturnedouttobeτ>b,()Fromwhichwecanseethatifτ=,namely,thereisnocouplingbetweenthevectorandthedilatonfield,therecouldalsoexistazeromodeThenwiththecondition(),thepotentialV(z)isvolcanolikeandPTlikeonesfor<b<andb=,respectivelyAndforb>,thepotentialwilldivergentattheboundaryoftheextradimensionwithτ=bb,butvanishwithτ=bbWeplottheshapesofthepotentialinFigzVHzLHb=LVHzLHb=LzVHzLHb=LVHzLHb=LzVHzLHb=LFIG:TheshapesofthepotentialsofthevectorfieldV(z)fordifferentparameterb,anda=,v=,τ=Underthecondition(),thezeromodeforthevectorfieldcanbeobtainedbysettingm=:ρe(bτ)A(z)()Inordertocheckwhetherthezeromodeforthevectorfieldcanbelocalizedonthebrane,wecaninvestigatewhetheritsatisfiestheorthonormalityconditionzbzbdzρm(z)ρn(z)=δmn(orymaxymaxdyeAρm(y)ρn(y)=δmn)Withrelationdz=e(b)Ady,wegetρdz=ρe(b)Adyeva(bbτ)ydyfory,()whichisinaccordwiththatinRefSoifthereisnocouplingbetweenthedilatonandthevectorfields,theorthonormalityconditionforthezeromodebecomesymaxymaxdyeAρ(y)ymaxymaxdy<,()whichisthesamewiththatinRefHoweveritisclearthatthezeromodeforthevectorfieldcanbelocalizedonthebrane,becausetheextradimensionyisfiniteWhileforthecasethatthereisacoupling,itcanbeobtainedfromtherelation()thattheconditionforthelocalizationofthezeromodeforthevectorfieldisτbfor<borτ>bforb>ΡHzLHb=LzΡHzLHb=LFIG:Theshapeofthezeromodeforvectorfieldρ(z)witha=,v=,τ=Becausethezeromodecanbelocalizedonthebranefordifferentb,sotherewillnounstableKKmodesForb<thereisnomassiveboundKKmodebutsomeresonancemayexistAndtherewillbefinitenumberofthemassiveboundKKmodesforb=,butinfiniteonesforb>BTheKalbRamondfieldsInthissubsectionweinvestigatetheKRfieldsTheactionofaKRfieldcoupledwiththedilatonisSKR=dxgeζpiHMNLHMNL,()whereHMNL=MBNListhefieldstrengthfortheKRfield,HMNL=gMOgNPgLQHOPQandζisthecouplingconstantTheequationsofmotionderivedfromthisactionandtheconformalmetric()read:eζpiµ(gHµαβ)(geζpiHαβ)=,()eζpiµ(gHµβ)=()IfwechoosethegaugeBα=andmakeadecompositionoftheKRfieldBαβ(n)(xλ,z)=nbˆαβ(n)(xλ)U(n)(z)e(ζ)A,wewillgetthefollowingSchrodingerequationfortheKKmodeUn(z):(zVKR(z))Un(z)=mnUn(z),()wheretheeffectivepotentialV(z)takesthefollowingformVKR=(bζ)A′bζA′′()ProvidedtheorthonormalityconditionzbzbdzUm(z)Un(z)=δmn,theactionoftheKRfield()isreducedtoSKR=ndxgˆ(gˆµ′µgˆα′αgˆβ′βhˆ(n)µ′α′β′hˆ(n)µαβmngˆα′αgˆβ′βbˆ(n)α′β′bˆ(n)αβ)()withhˆ(n)µαβ=µbˆαβthedimensionalfieldstrengthtensorTheexpressionoftheeffectivepotentialfortheKRfieldVKRcanbewrittenasthefunctionofy:VKR=e(b)AbζyA(bζ)(bζ)(b)(yA)()Sowiththebraneworldsolution(),thevaluesofthepotentialVKR(z)atz=andattheboundariesareVKR()=av(bζ)()andVKR(|z|zb)=av(bζ)(bζb)(va(b)z)()InordertogetnegativevalueofthepotentialVKR(z)atz=,theparameterζshouldsatisfyζ>b,()whichisnecessaryforthelocalizationofthezeromodeTherefore,itisclearthatthezeromodeoffreeKRfields(ζ=)cannotbelocalizedonthebrane,andthecouplingwiththedilatonfieldpiisnecessaryforthepurposeoflocalizingtheKRfieldzeromodeFromEq(),itcanbeseenthat,underthecondition(),thepotentialisavolcanolikeoneandaPTlikeonefor<b<andb=,respectivelyWhileforb>,thepotentialisdivergentattheboundaryz=zmaxwithζ=bb,butvanisheswithζ=bbWeplottheshapesofthepotentialforKRfieldKKmodesintheconformallyflatspacetimeinFigVKRHzLHb=,Ζ=LzVKRHzLHb=,Ζ=LVKRHzLHb=,Ζ=LzVKRHzLHb=,Ζ=LzVKRHzLHb=,Ζ=LzVKRHzLHb=,Ζ=LFIG:TheshapesofthepotentialsoftheKRfieldVKR(z)Theparametersaresettoa=,v=Sowiththecondition()wecanobtainazeromodefortheKRfieldbysettingm=:UebζA(z)()WealsoshouldcheckwhetherthezeromodefortheKRfieldscanbelocalizedonthebranethroughtheorthonormalityconditionzbzbdzU(z)<Withtherelationdz=e(b)AdywegetUdz=Ue(b)Adyeav(bζb)ydyfory()Thusonlywhenthecouplingconstantζsatisfiesζ>bforborζ>bbfor<b<,theintegralzbzbUdzisfinite,ie,thezeromodefortheKRfieldcanbelocalizedonthebraneTheshapeofthezeromodeforKRfieldisplottedinFigThespectrumstructureofKRKKmodesunderthecondition()issimilartothecaseofvectorfieldsUHzLHb=LzUHzLHb=LFIG:TheshapeofthezeromodeforKRfieldU(z)witha=,v=,ζ=CThespinfermionfieldsInthelastsubsection,weinvestigatethe

类似资料

编辑推荐

山河里客栈 《家乡益阳专辑》之三十三 .pdf

中国地图.pdf

道德经.txt

液压伺服系统.pdf

道教五派丹法精选第五集.pdf

职业精品

精彩专题

中秋节除了赏月,你还想怎么过?

“仰头望明月,寄情千里光”,算算你有多久没回家了。庆幸这个中秋节赶上了国庆节,不用悲伤“故乡再无春夏,只有秋冬”,独自一人赏月,8天长假,回家一趟,妥妥的!

用户评论

0/200
    暂无评论
上传我的资料

精选资料

热门资料排行换一换

  • 美容茶配方.doc

  • 永春白鹤拳师郑文龙 香港 李刚…

  • 成寒《英语,非学好不可》.pdf

  • 社会主义学说史.pdf

  • 神话的诗学.pdf

  • 图解巴菲特股票投资精粹.毛定娟.…

  • 中医-医学-本草纲目.pdf

  • [中]史册史伟着_手谈商战:围棋…

  • GB 23864-2009 防火…

  • 资料评价:

    / 22
    所需积分:0 立即下载

    意见
    反馈

    返回
    顶部