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

TL;DR

This paper investigates membrane dynamics in M/IIA theory, deriving non-perturbative two fermion terms in the effective action and matching supergravity calculations, revealing spin-orbit couplings and instanton effects.

Contribution

It provides the first non-perturbative derivation of membrane spin-orbit couplings including instanton corrections in the matrix theory framework.

Findings

Exact agreement between supergravity and matrix theory approaches.

Derivation of non-perturbative two fermion terms related to F^4 interactions.

Identification of membrane spin-orbit couplings in a curved background.

Abstract

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 F^4 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 two approaches when the background space-time is chosen to be that of the DLCQ M theory, which is asymptotically locally Anti-de Sitter.