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Boundary States and Black p-branes

Boundary States and Black p-branes. Shinpei Kobayashi （ RESCEU ） in collaboration with Tsuguhiko Asakawa (RIKEN) So Matsuura (RIKEN). 2004/05/19, 関東ゼミ. 1. Introduction.

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Boundary States and Black p-branes

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  1. Boundary States and Black p-branes Shinpei Kobayashi （RESCEU） in collaboration with Tsuguhiko Asakawa (RIKEN) So Matsuura (RIKEN) 2004/05/19, 関東ゼミ

  2. 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.

  3. X0 σ=0 σ=π τ Xi X D-brane • Open string endpoints can stick to D-brane • D-branes carry RR charges

  4. Dynamical non-BPS D-brane systems are very important in string theory, (e.g.) • D(2p+1)-brane in type IIA string • D(2p)-brane in type IIB string • D/anti D-brane system(c.f.) BPS D-branes, stable non-BPS D-brane But no one has succeeded in describing the dynamics of non-BPS D-brane.

  5. Non-BPS D-brane system (1)D(2p+1)-brane Closed string vacuum

  6. Non-BPS D-brane system (2)D/anti D-brane system closed string vacuum lower-dimensional D-brane

  7. Importance of dynamical D-brane systems • String theory • Searching for ‘real’ vacuum of string theory • String interaction & dynamics →non-perturbative string theory • Gravitation & Cosmology • D-brane inflation • Black hole evaporation 　 → Application to physics at Planck scale

  8. Trials to dynamical D-brane systems • Via ‘non-perturbative’ string theory • Open string field theory (A.Sen, …) • Closed string field theory (Asakawa, SK &Matsuura (’03), …) • Via conformal field theory • Logarithmic CFT description (Asakawa, Ishimoto, SK & Matsuura, work in progress)

  9. Trials to dynamical D-brane systems • Via low-energy effective theory(Zhou & Zhu (‘99), Ohta & Yokono (‘02) Brax, Mandal & Oz (‘01)) • Time-dependent solutions have not found yet. • Stable BPS solution →OK black p-branes : Today’s theme • Non-BPS solution → ?

  10. SUGRA String theory Dynamical system Hawking radiation, Inflation, etc. unknown object ? Unknown non-BPS black p-brane non-BPS D-brane (BPS) black p-brane BPS D-brane

  11. D-brane/black p-brane relation • Stable BPS D-brane case • (Unstable non-BPS case) • Black p-brane from boundary state (= D-brane) • (Difference between D-brane and black p-brane)

  12. 2. Black p-brane • Classical solution of SUGRA • It 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)

  13. String Theory and SUGRA String Field Theory action Supergravity action massless EOM EOM Classical solution of Sting theory Dp-brane Classical solution of SUGRA Black p-brane massless

  14. SUGRA action & ansatz ・Φ：dilaton ・ A：n-form potential ・ F：(n+1)-form field strength

  15. X0 σ=0 σ=π τ Xi X

  16. Black p-brane solution

  17. 3. Boundary state • D-brane in closed string channel • Source of closed strings← Such properties are guaranteed by conformal symmetry of the world-sheet conformal transformationζ→ f(ζ), where ζ=σ+iτ

  18. Using the conformal transformation, we can change the boundary condition for open strings into that for closed strings.

  19. Closed string Open string     D-brane Boundary state Open string 1-loop graph Closed string tree graph

  20. We can rewrite the boundary condition with using the oscillators.

  21. 4. Black p-brane solution from boundary state

  22. <B| |massless>

  23. (e.g.) dilaton (10-dim.) <B| |φ> +…

  24. We can extract each mode which are included in Φ, for example, dilaton, graviton, antisym.tensor and so on. • Such modes corresponds to the leading term of the classical solution.

  25. SFT action and source term

  26. <B| |> +… <B| |> + <B| Calculation of fields

  27. Here, we do not know how strings interact, so we use 3-point coupling of SUGRA. SFT SUGRA

  28. (e.g.) dilaton (10-dim.) <B| |φ> +… <B| |φ> + <B|

  29. ΦΦｈ A AΦ + A k1 k1 Φ Φ hμν k3 k3 Φ k2 k2 A

  30. Φ hμν k k

  31. (c.f.) SUGRA Φ hμν Bμν ・・・ + +…

  32. 5. Summary • Black 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 .

  33. 6. Problem • STF 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.

  34. 7. Future Works • We are now investigating... • Classical solution for unstable non-BPS D-brane • D-brane deformation using String Field Theory or CFT • Application • Hawking radiation in terms of D-brane • D/anti-D brane inflation

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