Supersymmetry of Noncompact MQCD-like Membrane Instantons and Heat Kernel Asymptotics

TL;DR

This paper analyzes the supersymmetry properties of noncompact membrane instantons in M-theory using heat kernel asymptotics, revealing residual supersymmetry through matching Seeley de-Witt coefficients.

Contribution

It provides a novel heat kernel asymptotics analysis of noncompact M2-brane instantons, demonstrating residual supersymmetry via matching spectral coefficients.

Findings

Eta-function Seeley de-Witt coefficients vanish.

Matching of zeta-function Seeley de-Witt coefficients up to quadratic order in zeta.

Evidence of residual supersymmetry in nonperturbative M-theory configurations.

Abstract

We perform a heat kernel asymptotics analysis of the nonperturbative superpotential obtained from wrapping of an M2-brane around a supersymmetric noncompact three-fold embedded in a (noncompact) G_2-manifold as obtained in [1], the three-fold being the one relevant to domain walls in Witten's MQCD [2], in the limit of small "zeta", a complex constant that appears in the Riemann surfaces relevant to defining the boundary conditions for the domain wall in MQCD. The MQCD-like configuration is interpretable, for small but non-zero zeta as a noncompact/"large" open membrane instanton, and for vanishing zeta, as the type IIA D0-brane (for vanishing M-theory cicle radius). We find that the eta-function Seeley de-Witt coefficients vanish, and we get a perfect match between the zeta-function Seeley de-Witt coefficients (up to terms quadratic in zeta) between the Dirac-type operator and one of the two Laplace-type operators figuring in the superpotential. This is an extremely strong signature of residual supersymmetry for the nonperturbative configurations in M-theory considered in this work.