Gravitational theory on Dbrane

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Gravitational theory on D-brane
Mini Workshop on Brane World 30-31 Oct. 2003
_at_TITech
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

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1. D-braneworld
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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
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From Probe D-brane to self-gravitating D-brane
Probe 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
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Theory
contains D3-brane solution
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2. Low energy effective equation/action for
Randall-Sundrum
Wiseman(2002), Kanno and Soda(2002), Shiromizu
and Koyama(2003)
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Recipe 1

• 1 Solve bulk spactimes by gradient expansion
• 2 Junction condition

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

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1. Solve the bulk
Gradient expansion
Solution
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2.Substitute the bulk solution into the original
action
3. Integrate over
4-dim. Einstein gravity
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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
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From Ten
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Junction condition
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Evolutional Eqs
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Gradient expansion(1)
0th order
Junction condition
solutions
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Gradient expansion (2)
1st order
Junction condition
Solutions
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adS/CFT point of view
(Solution to the Hamilton-Jacobi equation)
No Maxwell field part!
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4. Summary
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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

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Future study

• Z2 symmetry?
• Fermion?
• The action?

in preparation