Hamilton-Jacobi Method and Effective Actions of D-brane and M-brane in Supergravity

TL;DR

This paper demonstrates that the effective actions of D-branes and M-branes are solutions to Hamilton-Jacobi equations in supergravity, linking on-shell actions to supergravity solutions and aiding holographic studies.

Contribution

It shows that D-brane and M-brane effective actions solve Hamilton-Jacobi equations in supergravity, providing a new perspective on their on-shell nature and applications in holography.

Findings

Effective actions are solutions to H-J equations in supergravity.

Reproduction of supergravity solutions for D-branes and M-branes.

Application to gauge/gravity correspondence and supergravity solutions.

Abstract

We show that the effective actions of D-brane and M-brane are solutions to the Hamilton-Jacobi (H-J) equations in supergravities. This fact means that these effective actions are on-shell actions in supergravities. These solutions to the H-J equations reproduce the supergravity solutions that represent D-branes in a $B_2$ field, M2 branes and the M2-M5 bound states. The effective actions in these solutions are those of a probe D-brane and a probe M-brane. Our findings can be applied to the study of the gauge/gravity correspondence, especially the holographic renormalization group, and a search for new solutions of supergravity.