Boundary-States-and-Black-p-branes邊界狀態(tài)與黑P膜教學(xué)課件

1.IntroductionHowshouldweapplystringtheory

togravitationalsystems?

Whatis‘stringcosmology’?

→D-braneisthoughttobeakeytodescribewell-knowngravitationalsystemsviastringtheory.D-braneOpenstringendpointscanstickto

D-brane

D-branescarry

RRchargesX0XXi

σ=0

σ=π

τDynamicalnon-BPSD-branesystemsareveryimportantinstringtheory,(e.g.)D(2p+1)-braneintypeIIAstringD(2p)-braneintypeIIBstringD/antiD-branesystem

(c.f.)BPSD-branes,stablenon-BPSD-braneButnoonehassucceededindescribing

thedynamicsofnon-BPSD-brane.Non-BPSD-branesystem(1)

D(2p+1)-braneClosedstringvacuumNon-BPSD-branesystem(2)

D/antiD-branesystemclosedstringvacuumlower-dimensionalD-braneImportanceofdynamicalD-branesystemsStringtheorySearchingfor‘real’vacuumofstringtheoryStringinteraction&dynamics→non-perturbativestringtheoryGravitation&CosmologyD-braneinflationBlackholeevaporation→ApplicationtophysicsatPlanckscaleTrialstodynamicalD-branesystemsVia‘non-perturbative’stringtheoryOpenstringfieldtheory(A.Sen,…)Closedstringfieldtheory

(Asakawa,SK&Matsuura(’03),…)

ViaconformalfieldtheoryLogarithmicCFTdescription

(Asakawa,Ishimoto,SK&Matsuura,

workinprogress)TrialstodynamicalD-branesystemsVialow-energyeffectivetheory

(Zhou&Zhu(‘99),Ohta&Yokono(‘02)

Brax,Mandal&Oz(‘01))Time-dependentsolutionshavenotfoundyet.StableBPSsolution→OK

blackp-branes:Today’sthemeNon-BPSsolution→?DynamicalsystemHawkingradiation,Inflation,etc.unknownobjectSUGRAStringtheoryUnknownnon-BPSblackp-brane(BPS)blackp-branenon-BPSD-braneBPSD-brane?D-brane/blackp-branerelationStableBPSD-branecase(Unstablenon-BPScase)Blackp-brane

fromboundarystate(=D-brane)(DifferencebetweenD-brane

andblackp-brane)2.Blackp-braneClassicalsolutionofSUGRAIthassamesymmetry,chargeandmassasaD-brane→Low-energydescriptionofaD-brane.

Butnoonehasproved.(Non-BPSblackp-braneshavenotbeenfoundyet)StringTheoryandSUGRAStringFieldTheoryactionClassicalsolutionofStingtheoryDp-braneClassicalsolutionofSUGRABlackp-braneSupergravityactionmasslessmasslessEOMEOMSUGRAaction&ansatz?Φ：dilaton?A：n-formpotential?F：(n+1)-formfieldstrengthX0XXi

σ=0

σ=π

τBlackp-branesolution3.BoundarystateD-braneinclosedstringchannelSourceofclosedstrings

←Suchpropertiesareguaranteedby

conformalsymmetryoftheworld-sheet

conformaltransformation

ζ→f(ζ),whereζ=σ+iτUsingtheconformaltransformation,wecanchangetheboundaryconditionforopenstringsintothatforclosedstrings.ClosedstringBoundarystateClosedstringtreegraphOpenstringD-braneOpenstring1-loopgraphWecanrewritetheboundaryconditionwithusingtheoscillators.4.Blackp-branesolution

fromboundarystate<B||massless>(e.g.)dilaton(10-dim.)<B||φ>+…WecanextracteachmodewhichareincludedinΦ,forexample,dilaton,graviton,antisym.tensorandsoon.Suchmodescorrespondstotheleadingtermoftheclassicalsolution.SFTactionandsourcetermCalculationoffields<B||>+<B|<B||>+…Here,wedonotknowhowstringsinteract,soweuse3-pointcouplingofSUGRA.SUGRASFT(e.g.)dilaton(10-dim.)<B||φ>+<B|<B||φ>+…ΦΦｈAAΦ+hμνΦΦΦA(chǔ)Ak1k1k2k2k3k3kΦkhμν(c.f.)SUGRAΦhμνBμν???++…5.SummaryBlackp-branesaretheclassicalsolutionsofSUGRAandtheyarethoughttocorrespondtoD-branesinlowenergylimit.BoundarystatesareanotherrepresentationofD-branes,whicharewritteninclosedstringchannel.Using3-pointcouplingofSUGRA,wecanreproducetheasymptoticbehaviorofablackp-branefromaboundarystate.6.ProblemSTFcoupling?SUGRAcoupling?

Degreesoffreedomoffield-redefinition

gravitonofSFT?gravitonofSUGRA?

DifferencebetweenD-brane

andblackp-brane

→massivemodeeffect

→Hawkingradiati