Presentation on theme: "Open String Tachyon in Supergravity Solution"— Presentation transcript:
1 Open 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
2 MotivationWe 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.)
3 Contents D-branes and Classical Descriptions D/anti D-brane system Three-parameter solutionConclusionsDiscussions and Future Works
4 1. D-branes and Classical descriptions String Field TheorySupergravitylow energy limitα’ → 0classical description( Black p-brane )low energy limitD-brane( Boundary State )
5 D-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
7 BPS 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.
8 coincide 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
9 Boundary 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.
11 e.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.
12 String 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
13 We 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.
14 2. 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
17 Boundary state for D/anti D-brane with a constant tachyon vev RR-chargemass
18 Change 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).
19 Boundary state for D/anti D-brane constant tachyonRR-chargemass
20 3. 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
22 Property 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.
23 New parametrization → During the tachyon condensation, the RR-charge does not change its value. → We need a new parametrization suitable for t.c.
24 Asymptotic behavior of the three-parameter solution (= graviton, dilaton, RR-potential in SUGRA )
25 graviton, dilaton, RR-potential in string theory <B| |physical field>
29 Results and Comparison asymptotic behavior ofthe three-parameter solutionmassless modesvia the boundary state
30 We 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.
31 ConclusionsUsing 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.
32 Discussion : 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.
33 Wyman solution in Schwarzschild gauge Static, spherically symmetric, with a free scalar
34 Wyman solution in isotropic gauge r → RIn this gauge,we can compare it with the 3-para. sln.
35 Three-parameter solution case corresponds tothe dilaton charge.
36 Discussion : 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
37 We can not relate these parts with an ordinary boundary state counterpart ofthe D/anti D-brane system
38 Do 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
39 Construction of (Asakawa-Sugimoto-Terashima, JHEP 0302 (2003) 011) boundary interaction
40 →ordinary boundary state δ-function with ｔ → ∞→ordinary boundary state
41 From Gaussian Boundary State to BPS Dp-brane lower-dimensionalBPS D-branet → ∞tachyon has someconfiguration
42 -direction infinitely extend to-direction infinitelyGaussian in-directionlocalized at
43 Consider that each or is made from So far, we treat Consider that each or is made fromboundary state is deformed as follows:ordinaryDeformedoriginGaussian braneorigin
44 Gaussian boundary state D9-tachyonMixture of Neumann b.c. and Dirichlet b.c.→ smeared boundary condition
45 Oscillator pictureboundary condition in the oscillator picture
46 cf. ordinary boundary state open stringστclosedstringclosed tree graphτσboundary stateD-braneopen 1-loop graph
47 boundary conditions Longitudinal to the D-brane Transverse to the D-brane
48 Gaussian boundary state case ・ Longitudinal to the Dp-brane・Transverse to the Dp-brane
49 Oscillator part 0-mode part combine them to ordinary boundary state with ｔ→∞combine them
50 thus, in the limit （D9-tachyon vanishes） tension part via SFT（Kraus-Larsen, PRD63 (2001) ）From ato onethus, in the limit （D9-tachyon vanishes）
51 integrate with finitefinally, we obtainoriginGaussian braneorigin
57 Thus, we compare them as→ The effect of can be interpreted asD9-tachyon t.
58 Future 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)