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Supergravity Description of the Open String Tachyon

Supergravity Description of the Open String Tachyon. Shinpei Kobayashi ( RESCEU, University of Tokyo ). in collaboration with Tsuguhiko Asakawa and So Matsuura ( RIKEN ) . 2005/03/24 - 27 @ Tokyo University of Science, Noda, Chiba. 1. Introduction. D-brane

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Supergravity Description of the Open String Tachyon

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  1. Supergravity Description of the Open String Tachyon Shinpei Kobayashi ( RESCEU, University of Tokyo ) in collaboration with Tsuguhiko Asakawa and So Matsuura ( RIKEN ) 2005/03/24 - 27 @ Tokyo University of Science, Noda, Chiba

  2. 1. Introduction • D-brane • coherent state of closed string = boundary state • low energy → BH ? Our Universe ? • Non-BPSD-brane system • open string tachyon • decay into vacuum or other dimensional D-branes • low energy description ? We considered supergravity description of some DD-brane systems.

  3. Boundary State = D-brane

  4. open string tachyon or vacuum

  5. Supergravity Descriptions • Supergravity Descriptions= Spacetime made by a D-brane as a source • BPS Dp-brane → Black p-brane solution • Evidences • (ADM mass)=(RR-charge) ⇔ Dp-brane tension Tp • symmetry : SO(1,p)×SO(9-p) • long distance behavior = massless emission from Dp-brane boundary state (Di Vecchia et al. ‘97)

  6. Non-BPS case • Previous discussions [Brax-Mandal-Oz, Lu-Roy] • Three-parameter solution ⇔ DpDp-system • 3 parameters = Based on the behavior of the parameters. • Our Proposal • TP solution with ⇔ DpDp-system • TP solution with ⇔ Gaussian brane　　　　・・・ Based on long distance/boundary state correspondence

  7. Gravity String supergravity solution source = D-brane ? D-brane = boundary state Asymptotic behavior of supergravity solution Gravitons emitted from a D-brane Fluctuation from flat background

  8. Black p-brane solution • supergravity action • solution where

  9. <φ| |B> Gravity String long distance behavior Fourier Trans. massless emission

  10. Long distance behavior Black p-brane solution Three-parameter solution massless emission from D-brane BPS Dp-brane Non-BPS DD-system ・DpDp-system ・Gaussian brane ・・・ OK ?

  11. Point • New parametrization⇔ The value of the RR-charge does not change during the tachyon condensation. • Boundary state description of the tachyon condensation[Asakawa-Sugimoto-Terashima]→ We can directly compare the supergravity solution with the DD-system.

  12. same symmetry as system 2. Three-parameter solution (Zhou-Zhu, ’99) • action • isometry : SO(1, p)×SO(9-p) • asymptotically flat

  13. Three parameters General solution of symmetry SO(1,p)×SO(9-p) (Three-parameter solution) where “Physical quantities” RR-charge ADM mass Dilaton charge where

  14. Re-parametrization In the limit v →0 with fixed c_1 and μ_0, we get the black p-brane. ← fixed

  15. Long distance behavior

  16. 3. Boundary-like state • various DD-system = boundary-like state • RR-sector is unchanged • A, B, C : deformation parameters BPS Dp-brane : A=B=C=1 • 0-mode part : (p+1)-dim. object • oscillator part : no conformal inv. • only contributes to the massless mode

  17. <Φ| |B> Comparison • We can calculate the massless emission from the boundary-like state Gravity String

  18. (Asakawa-SK-Matsuura, ‘04) or p : unchanged

  19. Boundary state for DpDp • DpDp-bar system ~ TP solution with c_1 =0. • c_1 does not corresponds to the open string tachyon.

  20. Boundary State for Gaussian brane

  21. In the limit with fixed we have δ-function type 0-mode with non-trivial {A,B,C}:

  22. Asakawa-SK-Matsuura, in preparation. Dp-brane with a graduation

  23. Conclusion and Discussion • Conclusion • correspondence between the three-parameter solution and the DD-bar system. • long distance behavior / massless emission from the boundary state correspondence. • Re-parametrization {r_0,c_1,c_2} → to fix the RR-charge. • stringy counterpart of c_1 ~ the width of the brane made from D9D9-bar system the graduation of the brane made from D(-1)D(-1)-bar system

  24. Conclusion and Discussion • Discussion • other possibilities ? • geometry (horizon, stability,…) of the three-parameter solution ⇔ tachyon profiles ? • meaning of the dilaton charge • entropy counting for non-BPS systems • cosmological application(Takahashi-SK-Himemoto, work in progress)→ K.Takahashi’s talk

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