A Note on Fluxes and Superpotentials in M-theory Compactifications on Manifolds of G2 Holonomy
Chris Beasley, Edward Witten
Abstract
We consider the breaking of N=1 supersymmetry by non-zero G-flux when M-theory is compactified on a smooth manifold X of G2 holonomy. Gukov has proposed a superpotential W to describe this breaking in the low-energy effective theory. We check this proposal by comparing the bosonic potential implied by W with the corresponding potential deduced from the eleven-dimensional supergravity action. One interesting aspect of this check is that, though W depends explicitly only on G-flux supported on X, W also describes the breaking of supersymmetry by G-flux transverse to X.
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