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1.Introduction How should we apply string theory to gravitational systems?What is string cosmology?D-brane is thought to be a key to describe well-known gravitational systems via string theory.D-braneOpen string endpoints can stick to D-braneD-branes carry RR chargesX0XXi=0=Dynamical non-BPS D-brane systems are very important in string theory,(e.g.)D(2p+1)-brane in type IIA stringD(2p+1)-brane in type IIA stringD(2p)-brane in type IIB stringD(2p)-brane in type IIB stringD/anti D-brane systemD/anti D-brane system(c.f.)BPS D-branes,(c.f.)BPS D-branes,stablestable non-BPS D-brane non-BPS D-braneBut no one has succeeded in describing the dynamics of non-BPS D-brane.Non-BPS D-brane system(1)D(2p+1)-braneClosed string vacuumNon-BPS D-brane system(2)D/anti D-brane systemclosed string vacuumlower-dimensional D-brane Importance of dynamical D-brane systemsString theorySearching for real vacuum of string theorySearching for real vacuum of string theoryString interaction&dynamicsString interaction&dynamics non-perturbative string theoryGravitation&CosmologyD-brane inflationD-brane inflationBlack hole evaporation Black hole evaporation Application to physics at Planck scaleTrials to dynamical D-brane systemsVia non-perturbative string theoryOpen string field theory (A.Sen,)Open string field theory (A.Sen,)Closed string field theory Closed string field theory (Asakawa,SK&Matsuura(03),)(Asakawa,SK&Matsuura(03),)Via conformal field theoryLogarithmic CFT description Logarithmic CFT description(Asakawa,Ishimoto,SK&Matsuura,(Asakawa,Ishimoto,SK&Matsuura,work in progress)work in progress)Trials to dynamical D-brane systemsVia low-energy effective theory (Zhou&Zhu(99),Ohta&Yokono(02)Brax,Mandal&Oz(01)Time-dependent solutions have not found yet.Time-dependent solutions have not found yet.Stable BPS solution Stable BPS solution OKOK black p-branes:Todays themeNon-BPS solution?Non-BPS solution?Dynamical systemHawking radiation,Inflation,etc.unknownobjectSUGRAString theoryUnknown non-BPSblack p-brane(BPS)black p-branenon-BPS D-braneBPS D-brane?D-brane/black p-brane relationStable BPS D-brane caseStable BPS D-brane case(Unstable non-BPS case)(Unstable non-BPS case)Black p-brane from boundary state(=D-brane)(Difference between D-brane and black p-brane)2.Black p-brane Classical solution of SUGRAIt has same symmetry,charge and mass as a D-brane Low-energy description of a D-brane.But no one has proved.(Non-BPS black p-branes have not been found yet)String Theory and SUGRAString Field Theory actionClassical solution ofSting theoryDp-braneClassical solution ofSUGRABlack p-braneSupergravity actionmasslessmasslessEOMEOMSUGRA action&ansatz：dilaton A：n-form potential F：(n+1)-form field strengthX0XXi=0=Black p-brane solution3.Boundary stateD-brane in closed string channelSource of closed strings Such properties are guaranteed by conformal symmetry of the world-sheet conformal transformation f(),where=+iUsing the conformal transformation,we can change the boundary condition for open strings into that for closed strings.Closed stringBoundary stateClosed string tree graphOpen stringD-braneOpen string 1-loop graphWe can rewrite the boundary condition with using the oscillators.4.Black p-brane solution from boundary state (e.g.)dilaton(10-dim.)+We can extract each mode which are included in,for example,dilaton,graviton,antisym.tensor and so on.Such modes corresponds to the leading term of the classical solution.SFT action and source termCalculation of fields +B|+Here,we do not know how strings interact,so we use 3-point coupling of SUGRA.SUGRASFT(e.g.)dilaton(10-dim.)+B|+A A+hAAk1k1k2k2k3k3kkh(c.f.)SUGRAhB+5.SummaryBlack p-branes are the classical solutions of SUGRA and they are thought to correspond to D-branes in low energy limit.Boundary states are another representation of D-branes,which are written in closed string channel.Using 3-point coupling of SUGRA,we can reproduce the asymptotic behavior of a black p-brane from a boundary state.6.ProblemSTF coupling SUGRA coupling?Degrees of freedom of field-redefinitiongraviton of SFT graviton of SUGRA?Difference between D-brane and black p-brane massive mode effect Hawking radiation,etc.7.Future WorksWe are now investigating.Classical solution for unstable non-BPS D-Classical solution for unstable non-BPS D-branebraneD-brane deformation using String Field D-brane deformation using String Field Theory or CFTTheory or CFTApplicationHawking radiation in terms of D-braneHawking radiation in terms of D-braneD/anti-D brane inflationD/anti-D brane inflation
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