Presentation on theme: "Open String Tachyon in Supergravity Solution"— Presentation transcript:
1Open String Tachyon in Supergravity Solution Shinpei Kobayashi( Research Center for the Early Universe, The University of Tokyo )Based on hep-th/in collaboration withTsuguhiko Asakawa and So Matsuura ( RIKEN )2005/01/18at KEK
2MotivationWe would like to apply the string theory to the analyses of the gravitational systems.We have to knowhow we should apply string theory to realistic gravitational systems,or what stringy (non-perturbative) effects are,or what stringy counterparts of the BHs or Universe in the general relativity are.→ D-branes may be a clue to tackle such problems (BH entropy, D-brane inflation, etc.)
3Contents D-branes and Classical Descriptions D/anti D-brane system Three-parameter solutionConclusionsDiscussions and Future Works
41. D-branes and Classical descriptions String Field TheorySupergravitylow energy limitα’ → 0classical description( Black p-brane )low energy limitD-brane( Boundary State )
5D-brane ( BPS case ) Open string endpoints stick to a D-brane PropertiesSO(1,p)×SO(9-p) ( BPS case ), RR-charged(mass) 1/(string coupling)Dp-braneX0XμXiopen string
7BPS black p-brane solution (D=10) ・ SO(1,p)×SO(9-p),・ (mass)=(RR-charge), which are the same as D-branesit must be large forthe validity of SUGRADi Vecchia et al. suggested more direct method to checkthe correspondence between a Dp-braneand a black p-brane solution using the boundary state.
8coincide Relation between the D-brane ( the boundary state) and the black p-brane solution(Di Vecchia et al. (1997))asymptotic behavior of the black p-brane = difference from the flat background = graviton, dilaton, RR-potential in SUGRAmassless modes of the closed strings from the boundary state ( D-brane in closed string channel ) = graviton, dilaton, RR-potential in string theory( string field theory )coincide
9Boundary State ( = D-brane) Boundary states are defined as sources of closed strings ( = D-branes in closed string channel ).As closed strings include gravitons, the boundary state directly relates to a black p-brane solution.
11e.g. ) asymptotic behavior of Φ of black p-brane leading term at infinitycoincident<B| |φ>We can reproduce the leading term of a black p-branesolution ( asymptotic behavior ) via the boundary state.
12String Field Theory Supergravity eom eom D-brane ( Boundary State ) low energy limitα’ → 0eomeomD-brane( Boundary State )classical solution( Black p-brane )low energy limitBPS case → OK (Di Vecchia et al. (1997))non-BPS case → ?We study non-BPS systems( e.g. D/anti D-brane system ).non-BPS casesare more realisticin GR sense
13We verify their claim using the boundary state. BPS caseDp-brane black p-braneNon-BPS caseD/anti D-brane system with a constant tachyon vev Three-parameter solution ? ( guessed by Brax-Mandal-Oz (2000))( other non-BPS system corresponding classical solution ?)We verify their claim using the boundary state.
142. D/anti D-brane system tachyon condensation closed string emission D-branes andanti D-branesattracts togetherUnstable multiple branesOpen string tachyonrepresents its instabilityStableD-branes are left case
17Boundary state for D/anti D-brane with a constant tachyon vev RR-chargemass
18Change of the Mass during the tachyon condensation D-branes, anti D-branes coincide with each other. ( t = 0 ) During the tachyon condensation ( t = t0 ) tachyon vev is included in the mass.Final state ( t = ∞ ) The mass will decrease through the closed string emission, and the value of the mass will coincide with that of the RR-charge (BPS).
19Boundary state for D/anti D-brane constant tachyonRR-chargemass
203. Three-parameter solution ( Zhou & Zhu (1999) ) SUGRA actionansatz : SO(1, p)×SO(9-p) ( D=10 )same symmetry as the D/anti D-brane system
22Property of the three-parameter solution ADM massRR chargeWe can extend it to an arbitrary dimensionality.We re-examine the correspondencebetween the D/anti D-brane systemandthe three-parameter solutionusing the boundary state.~?~?From the form of the boundary state,Brax-Mandal-Oz claimedthat c_1 corresponds to the tachyon vev.
23New parametrization → During the tachyon condensation, the RR-charge does not change its value. → We need a new parametrization suitable for t.c.
24Asymptotic behavior of the three-parameter solution (= graviton, dilaton, RR-potential in SUGRA )
25graviton, dilaton, RR-potential in string theory <B| |physical field>
29Results and Comparison asymptotic behavior ofthe three-parameter solutionmassless modesvia the boundary state
30We find that they coincide with each other under the following identification, RR-charge, constant duringthe tachyon condensationv ^2 ~ M^2 – Q^2: non-extremality→ tachyon vev can be seen asa part of the ADM massc_1 does not corresponds tothe vev of the open string tachyon.The three-parameter solution with c_1=0does correspond to the D/anti D-brane system.
31ConclusionsUsing the boundary state, we find that the three-parameter solution with c_1=0 corresponds to the D/anti D-brane system with a constant tachyon vev.New parametrization is needed to keep the RR-charge constant during the tachyon condensation.The vev of the open string tachyon is only seen as a part of the ADM mass.c_1 does not corresponds to the tachyon vev as opposed to the proposal made so far.We find that we can extend the correspondence between D-branes and classical solutions to non-BPS case.First discovery of the correspondence in non-BPS case.It may be a clue to describe “realistic” gravitational systems which are generally non-BPS.
32Discussion : Why was c_1 thought to be the open string tachyon vev ? Parametrization → during the t.c., the RR-charge does not change its value. →The relation between the mass and the scalar charge → cf. Wyman solution in D=4 case c_1 corresponds to the dilaton charge.
33Wyman solution in Schwarzschild gauge Static, spherically symmetric, with a free scalar
34Wyman solution in isotropic gauge r → RIn this gauge,we can compare it with the 3-para. sln.
35Three-parameter solution case corresponds tothe dilaton charge.
36Discussion : Stringy counterpart of c_1 ? has something to do with the brane.We can not relate these partswith an ordinaryboundary statecounterpart ofthe D/anti D-brane system
37We can not relate these parts with an ordinary boundary state counterpart ofthe D/anti D-brane system
38Do we have such a deformation in string theory ? Deformation of the boundary stateDo we have such a deformationin string theory ?→ with open string tachyonWe can reproduce the 3-para. sln with non-zeroby adjusting α・β
39Construction of (Asakawa-Sugimoto-Terashima, JHEP 0302 (2003) 011) boundary interaction
40→ordinary boundary state δ-function with ｔ → ∞→ordinary boundary state
41From Gaussian Boundary State to BPS Dp-brane lower-dimensionalBPS D-branet → ∞tachyon has someconfiguration
42-direction infinitely extend to-direction infinitelyGaussian in-directionlocalized at
43Consider that each or is made from So far, we treat Consider that each or is made fromboundary state is deformed as follows:ordinaryDeformedoriginGaussian braneorigin
44Gaussian boundary state D9-tachyonMixture of Neumann b.c. and Dirichlet b.c.→ smeared boundary condition
45Oscillator pictureboundary condition in the oscillator picture
46cf. ordinary boundary state open stringστclosedstringclosed tree graphτσboundary stateD-braneopen 1-loop graph
47boundary conditions Longitudinal to the D-brane Transverse to the D-brane
48Gaussian boundary state case ・ Longitudinal to the Dp-brane・Transverse to the Dp-brane
49Oscillator part 0-mode part combine them to ordinary boundary state with ｔ→∞combine them
50thus, in the limit （D9-tachyon vanishes） tension part via SFT（Kraus-Larsen, PRD63 (2001) ）From ato onethus, in the limit （D9-tachyon vanishes）
51integrate with finitefinally, we obtainoriginGaussian braneorigin
57Thus, we compare them as→ The effect of can be interpreted asD9-tachyon t.
58Future Workc_1 and a Gaussian brane (SK, Asakawa & Matsuura, hep-th/0502XXX )Entropy counting via non-BPS boundary stateConstruction of a time-dependent solutionfeedback to SFTSolving δB|B>=0 ( E-M conservation law in SFT ) (Asakawa, SK & Matsuura, JHEP 0310 (2003) 023)Application to cosmology (SK, K. Takahashi & Himemoto)Stability analysis ( K. Takahashi & SK)