A Note on Hamilton-Jacobi Formalism and D-brane Effective Actions
Matsuo Sato, Asato Tsuchiya
TL;DR
This paper reviews the Hamilton-Jacobi formalism for gravitational and flat space systems and discusses how D-brane and M-brane effective actions relate to supergravity on-shell actions.
Contribution
It extends the Hamilton-Jacobi formalism to include D-brane and M-brane effective actions as on-shell supergravity actions.
Findings
Hamilton-Jacobi equations derived for on-shell actions.
Comparison between gravitational and flat space cases.
D-brane and M-brane actions identified as supergravity on-shell actions.
Abstract
We first review the canonical formalism with general space-like hypersurfaces developed by Dirac by rederiving the Hamilton-Jacobi equations which are satisfied by on-shell actions defined on such hypersurfaces. We compare the case of gravitational systems with that of the flat space. Next, we remark as a supplement to our previous results that the effective actions of D-brane and M-brane given by arbitrary embedding functions are on-shell actions of supergravities.
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