### 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 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.

Original language | English |
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Pages (from-to) | 685-702 |

Number of pages | 18 |

Journal | Nuclear Physics B |

Volume | 551 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1999 Jul 5 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*551*(3), 685-702. https://doi.org/10.1016/S0550-3213(99)00233-3