Superpotentials and Membrane Instantons

Details Superpotentials and Membrane Instantons Superpotentials and Membrane Instantons

1999-07-06

arxiv.org/abs/hep-th/9907026v1

Physics

High Energy Physics

High Energy Physics - Theory

harvmac, no figs, 24 pp (l mode)

Scientific paper

We investigate nonperturbative effects in M-theory compactifications arising from wrapped membranes. In particular, we show that in $d=4, \CN=1$ compactifications along manifolds of $G_2$ holonomy, membranes wrapped on rigid supersymmetric 3-cycles induce nonzero corrections to the superpotential. Thus, membrane instantons destabilize many M-theory compactifications. Our computation shows that the low energy description of membrane physics is usefully described in terms of three-dimensional topological field theories, and the superpotential is expressed in terms of topological invariants of the 3-cycle. We discuss briefly some applications of these results. For example, using mirror symmetry we derive a counting formula for supersymmetric three-cycles in certain Calabi-Yau manifolds.

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