1. Gravitational theory on D-brane
Mini Workshop on Brane World Oct.
Gravitational theory on D-brane
Tokyo Institute of Technology
Tetsuya Shiromizu
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
Mirage Cosmology
Branonium
D-Brane Chemistry
Dp-brane
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 0th 1st Constant of integration Kazulza-Klein mode
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 No Maxwell field part!
(Solution to the Hamilton-Jacobi equation)
No Maxwell field part!

22. 4. Summary

23. Summary
・Gravitational theory on self-gravitating D-brane (with Z2 symmetry)
・Not like Einstein-Maxwell theory
・Maxwell field does not couple to the gravity on the brane!?
・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

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