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Gravitational theory on D-brane

Mini Workshop on Brane World 30-31 Oct. 2003 @TITech. Gravitational theory on D-brane. Tetsuya Shiromizu. Tokyo Institute of Technology. Shiromizu,Koyama,Onda,Torii, Phys. Rev. D68,063506(2003) Shiromizu,Koyama,Torii, to appear in Phys. Rev. D(2003)

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Gravitational theory on D-brane

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  1. Mini Workshop on Brane World 30-31 Oct. 2003 @TITech Gravitational theory on D-brane Tetsuya Shiromizu Tokyo Institute of Technology Shiromizu,Koyama,Onda,Torii, Phys. Rev. D68,063506(2003) Shiromizu,Koyama,Torii, to appear in Phys. Rev. D(2003) Onda,Shiromizu,Koyama,Hayakawa, in preparation

  2. Outline • D-braneworld • Effective theory for Randall-Sundrum model • Gravitational equation on D-brane • Summary

  3. 1. D-braneworld

  4. D-brane and braneworld One motivation for braneworld: Closed string Open string D-brane Be serious about D-brane! Bulk spacetime supergravity Brane Born-Infeld action

  5. From Probe D-brane to self-gravitating D-brane Probe D-brane Dp-brane Mirage Cosmology Branonium D-Brane Chemistry Kehagias and Kiritsis(1999),… Burgess et al (2003), Takahashi and Ichikawa(2003) Burgess et al (2003) Dq-brane Think of self-gravity of D-brane carefully! For very early universe and black holes

  6. Theory contains D3-brane solution

  7. 2. Low energy effective equation/action for Randall-Sundrum Wiseman(2002), Kanno and Soda(2002), Shiromizu and Koyama(2003)

  8. Recipe 1 1 Solve bulk spactimes by gradient expansion 2 Junction condition

  9. Derivation Junction condition 0th solution 1st Shiromizu,Maeda,Sasaki(2000) Constant of integration Kazulza-Klein mode

  10. Recipe 2 :4d effective action from 5d original action • Solve the bulk spacetime under long-wave approximation • Substitute the bulk field solution satisfying the junction condition into the original action • Integrate the action over the direction of extra dimensions

  11. 1. Solve the bulk Gradient expansion Solution

  12. 2.Substitute the bulk solution into the original action 3. Integrate over … 4-dim. Einstein gravity

  13. 3. Gravitational equation on D-brane Shiromizu,Koyama,Onda,Torii, Phys. Rev. D68,063506(2003) Shiromizu,Koyama,Torii, to appear in Phys. Rev. D(2003) Onda,Shiromizu,Koyama,Hayakawa, in preparation

  14. Theory

  15. From Ten

  16. Junction condition

  17. Evolutional Eqs

  18. Gradient expansion(1) 0th order Junction condition solutions

  19. Gradient expansion (2) 1st order Junction condition Solutions

  20. adS/CFT point of view (Solution to the Hamilton-Jacobi equation) No Maxwell field part!

  21. 4. Summary

  22. Summary ・Gravitational theory on self-gravitating D-brane (with Z2 symmetry) ・If RS tuning is not required, Maxwell field will couple to the gravity on the brane. ・The Gravitational constant is propotional to cosmological constant on brane ・Not like Einstein-Maxwell theory ・Maxwell field does not couple to the gravity on the brane!?

  23. Future study ・Z2 symmetry? ・Fermion? ・The action? in preparation

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