Born-Infeld Action from Supergravity

TL;DR

This paper demonstrates that the Born-Infeld action with Wess-Zumino terms for Ramond-Ramond fields solves the Hamilton-Jacobi equation in type IIB supergravity, linking supergravity solutions to D3-brane effective actions and holographic RG flows.

Contribution

It derives the D3-brane effective action as a solution to the Hamilton-Jacobi equation in supergravity, connecting supergravity solutions to D-brane dynamics and holography.

Findings

Reproduces on-shell actions for D3-branes in supergravity.

Shows the Born-Infeld action solves the H-J equation in type IIB supergravity.

Connects supergravity solutions to noncommutative Yang-Mills and AdS/CFT correspondence.

Abstract

We show that the Born-Infeld action with the Wess-Zumino terms for the Ramond-Ramond fields, which is the D3-brane effective action, is a solution to the Hamilton-Jacobi (H-J) equation of type IIB supergravity. Adopting the radial coordinate as time, we develop the ADM formalism for type IIB supergravity reduced on $S^5$ and derive the H-J equation, which is the classical limit of the Wheeler-De Witt equation and whose solutions are classical on-shell actions. The solution to the H-J equation reproduces the on-shell actions for the supergravity solution of a stack of D3-branes in a $B_2$ field and the near-horizon limit of this supergravity solution, which is conjectured to be dual to noncommutative Yang Mills and reduces to $AdS_5 \times S^5$ in the commutative limit. Our D3-brane effective action is that of a probe D3-brane, and the radial time corresponds to the vacuum expectation value of the Higgs field in the dual Yang Mills. Our findings can be applied to the study of the holographic renormalization group.