1 / 37

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.

harding-fry
Télécharger la présentation

Boundary States and Black p-branes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related