TL;DR
This paper derives the Wheeler-De Witt equation for a D3-brane embedded in supergravity background, providing analytical solutions and tunneling probabilities, advancing understanding of quantum brane gravity.
Contribution
It introduces the Wheeler-De Witt equation for brane gravity with analytical solutions and tunneling probability calculations, a novel approach in this context.
Findings
Analytical solutions to the Wheeler-De Witt equation for D3-brane system.
Calculation of tunneling probability from Planckian to classical regime.
Insights into quantum effects in brane gravity.
Abstract
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.
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