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

Kanishka Belani·Payal Kaura·Aalok Misra
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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.

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Kanishka Belani, Payal Kaura, Aalok Misra. 2006-09-20. Supersymmetry of Noncompact MQCD-like Membrane Instantons and Heat Kernel Asymptotics. https://doi.org/10.1088/1126-6708%2F2006%2F10%2F023

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