Membrane instantons are constituted by supermembranes (M2-branes) wrapped on spacelike (and supersymmetric) cycles. These appear as non-perturvative effects in M-theory model building. For instance they generate the gauge hierarchy in constructions of M-theory on G2-manifolds such as the G2-MSSM.
Basically the effect is that the action functional of the given 11-dimensional supergravity is multiplied by the exponentiated Nambu-Goto action of the wrapping membrane configurations $\phi \colon \Sigma \to X$. These are of the form (e.g. Harvey-Moore 99, (4.13), Atiyah-Witten 01 (4.17), Curio 02, (2.15))
where $\ell_P$ is the Planck length of 11-dimensional supergravity, $T = 1/\ell^3$ is the membrane tension, $C$ is the background supergravity C-field, $g$ the background metric and $vol$ its volume form, .
Under the duality between M-theory and type IIA string theory, membrane instantons become string worldsheet instantons or D-brane instantons, depending on whether they wrapped brane wrape the M-theory circle fiber or not. See at non-perturbative effect the section Worldsheet and brane instantons for more.
When here $(\Sigma, \phi^\ast g)$ is a hyperbolic 3-manifold and $\phi^\ast C = CS(\omega)$ is the Chern-Simons invariant then this is the exponentiated “complex volume” of $\Sigma$^{1}.
Katrin Becker, Melanie Becker, Andrew Strominger, section 2.1 of Five-branes, membranes and nonperturbative string theory, Nucl. Phys. B 456, 130 (1995) (hep-th/9507158)
Jeff Harvey, Greg Moore, Superpotentials and Membrane Instantons (arXiv:hep-th/9907026, spire:503172)
Discussion specifically for M-theory on G2-manifolds includes
Michael Atiyah, Edward Witten, around (4.17) of $M$-Theory dynamics on a manifold of $G_2$-holonomy, Adv. Theor. Math. Phys. 6 (2001) (arXiv:hep-th/0107177)
Gottfried Curio, Superpotentials for M-theory on a $G_2$ holonomy manifold and Triality symmetry, JHEP 0303:024,2003 (arXiv:hep-th/0212211)
Discussion related to the cosmological constant in models of M-theory on G2-manifolds includes
which concludes that with taking non-perturbative effects from membrane instantons into account one gets 4d vacua with vanishing and negative cosmological constant (Minkowski spacetime and anti-de Sitter spacetime) but not with positive cosmological constant (de Sitter spacetime). They close by speculating that M5-brane instantons might yield de Sitter spacetime.
This relation was pointed out by Hisham Sati. ↩
Last revised on February 13, 2019 at 09:55:45. See the history of this page for a list of all contributions to it.