Explicit scale-separated dS5 maximum in M-theory on a 6D Riemann-flat manifold with vacuum energy 10^{-8} in Planck units, obtained via Casimir energies and fluxes.
Superpotentials and Membrane Instantons
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abstract
We investigate nonperturbative effects in M-theory compactifications arising from wrapped membranes. In particular, we show that in $d=4, \mathcal{N}=1$ 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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BPS conditions for M2-branes wrapping cycles in weak G2 manifolds are equivalent to associativity, with one-loop effects for invariant cycles in Sasaki-Einstein orbifolds expressed via equivariant indices and recovering known S3/Zk results.
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An M-theory dS maximum from Casimir energies on Riemann-flat manifolds
Explicit scale-separated dS5 maximum in M-theory on a 6D Riemann-flat manifold with vacuum energy 10^{-8} in Planck units, obtained via Casimir energies and fluxes.
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Membrane instantons and non-perturbative effects in $\mathrm{AdS}_{4}/\mathrm{CFT}_{3}$
BPS conditions for M2-branes wrapping cycles in weak G2 manifolds are equivalent to associativity, with one-loop effects for invariant cycles in Sasaki-Einstein orbifolds expressed via equivariant indices and recovering known S3/Zk results.