Hamilton–Jacobi method and effective actions of D-brane and M-brane in supergravity Original Research Article

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 B2 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.