Non-perturbative membrane spin-orbit couplings in M/IIA theory

Membrane source-probe dynamics is investigated in the framework of the finite N-sector DLCQ M-theory compactified on a transverse two-torus for an arbitrary size of the longitudinal dimension. The non-perturbative two-fermion terms in the effective action of the matrix theory, the (2 + 1 )-dimensional supersymmetric Yang-Mills theory, that are related to the four derivative F⁴ terms by the supersymmetry transformation are obtained, including the one-loop term and full instanton corrections. On the supergravity side, we compute the classical probe action up to two-fermion terms based on the classical supermembrane formulation in an arbitrary curved background geometry produced by source membranes satisfying the BPS condition; two-fermion terms correspond to the spin-orbit couplings for membranes. We find precise agreement between the two approaches when the background space-time is chosen to be that of the DLCQ M-theory, which is asymptotically locally anti-de Sitter.