Wheeler-De Witt equation for brane gravity
  We consider the gravity in the system consisting of the Bogomol'nyi-Prasad-Sommerfield (BPS) D3-brane embedded in the flat background geometry, produced by the solutions of the supergravity. The effective action for this system is represented by the sum of the Hilbert-Einstein and DBI actions. We derive the Wheeler-De Witt equation for this system and obtain analytical solutions in some special cases. We also calculate tunneling probability from Planckian size of D3-brane to the classical regime. 
Pawel Gusin