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

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.

23 pages, Latex, no figuress, improved presentation, references updated; to appear in Nucl.Phys.B

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• M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory
• A Nonperturbative Test of M2-Brane Theory
• Instantons, Compactification and S-duality in N=4 SUSY Yang-Mills Theory I
• Instantons, Compactification and S-duality in N=4 SUSY Yang-Mills Theory II
• Eleven-dimensional massless superparticles and matrix theory spin-orbit couplings revisited
• Structure in Supersymmetric Yang-Mills Theory
• Supersymmetry of Green-Schwarz Superstring and Matrix String Theory
• The SU(N) Matrix Model at Two Loops
• Green-Schwarz Superstring Action in Type IIA Supergravity Backgrounds