nLab
membrane instanton

Contents

Contents

Idea

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 ϕ:ΣX\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))

exp( Σ( P 3vol(ϕ *g)+iϕ *C)), \exp\left( \int_{\Sigma} \left( \ell_P^{-3} vol(\phi^\ast g) + i \phi^\ast C \right) \right) \,,

where P\ell_P is the Planck length of 11-dimensional supergravity, T=1/ 3T = 1/\ell^3 is the membrane tension, CC is the background supergravity C-field, gg the background metric and volvol its volume form, .

Properties

Relation to worldsheet and D-brane instantons

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.

Relation to complex volume

When here (Σ,ϕ *g)(\Sigma, \phi^\ast g) is a hyperbolic 3-manifold and ϕ *C=CS(ω)\phi^\ast C = CS(\omega) is the Chern-Simons invariant then this is the exponentiated “complex volume” of Σ\Sigma1.

References

Discussion specifically for M-theory on G2-manifolds includes

Discussion related to the cosmological constant in models of M-theory on G2-manifolds includes

  • Beatriz de Carlos, Andre Lukas, Stephen Morris, Non-perturbative vacua for M-theory on G2 manifolds, JHEP 0412:018, 2004 (arxiv:hep-th/0409255)

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.


  1. This relation was pointed out by Hisham Sati.

Last revised on September 8, 2018 at 13:44:01. See the history of this page for a list of all contributions to it.