We will consider the following effective action of string theory in leading order of $\alpha'$:
$$S=\frac{1}{2\kappa^2_0}\int d^{D}X\sqrt{-G}e^{-2\Phi}\left[R-2\Lambda-\frac{1}{12}H_{\mu\nu\lambda}H^{\mu\nu\lambda}+4\partial_{\mu}\Phi\partial^{\mu}\Phi\right].$$
Is there is an analogous Hamiltonian formalism to this action, as was done for Einstein-Hilbert action of GR fall under the umbrella of the ADM formalism?
For example: How to present the surface term to this action? What is the analog of the extrinsic curvature? And the induced metric for the $B$ field which expressed through the 3-form $H$ in this action? How the dilaton is contribute to the surface term?
and especially what is the ADM mass (energy) formula which we will obtain using the ADM formalism on the string low energy effective action in a reference frame of a flat and general spacetime?
