Effective Action for Membrane Dynamics in DLCQ $M$ theory on a Two-torus

Details Effective Action for Membrane Dynamics in DLCQ $M$ theory on a Two-torus Effective Action for Membrane Dynamics in DLCQ $M$ theory on a Two-torus

1998-08-30

arxiv.org/abs/hep-th/9808183v1

Phys.Rev.D59:021901,1999

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, latex, no figures

Scientific paper

10.1103/PhysRevD.59.021901

The effective action for the membrane dynamics on the background geometry of the $N$-sector DLCQ $M$ theory compactified on a two-torus is computed via supergravity. We compare it to the effective action obtained from the matrix theory, i.e., the (2+1)-dimensional supersymmetric Yang-Mills (SYM) theory, including the one-loop perturbative and full non-perturbative instanton effects. Consistent with the DLCQ prescription of $M$ theory {\em a la} Susskind, we find the precise agreement for the finite $N$-sector (off-conformal regime), as well as for the large $N$ limit (conformal regime), providing us with a concrete example of the correspondence between the matrix theory and the DLCQ $M$ theory. Non-perturbative instanton effects in the SYM theory conspire to yield the eleven-dimensionally covariant effective action.

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