Supersymmetry of noncompact MQCD-like membrane instantons and heat kernel asymptotics

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) G2-manifold as obtained, the three-fold being the one relevant to domain walls in Witten's MQCD, in the limit of small 'ζ', 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 ζ as a noncompact/'large open membrane instanton, and for vanishing ζ, as the type IIA D0-brane (for vanishing M-theory circle 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 ζ) between the Dirac-type operator and one of the two Laplace-type operators figuring in the superpotential. Given the dissimilar forms of the bosonic and the square of the fermionic operators, this is an extremely nontrivial check, from a spectral analysis point of view, of the expected residual supersymmetry for the nonperturbative configurations in M-theory considered in this work