MQCD, ("BARELY") G2 MANIFOLDS AND (ORIENTIFOLD OF) A COMPACT CALABI–YAU

Abstract

We begin with a discussion on two apparently disconnected topics — one related to nonperturbative superpotential generated from wrapping an M2-brane around a supersymmetric three cycle embedded in a G2-manifold evaluated by the path-integral inside a path-integral approach of Ref. 1, and the other centered around the compact Calabi–Yau CY3(3, 243) expressed as a blow-up of a degree-24 Fermat hypersurface in WCP4[1, 1, 2, 8, 12]. For the former, we compare the results with the ones of Witten on heterotic worldsheet instantons.2 The subtopics covered in the latter include an 𝒩=1 triality between Heterotic, M- and F-theories, evaluation of RP2-instanton superpotential, Picard–Fuchs equation for the mirror Landau–Ginzburg model corresponding to CY3(3, 243), D = 11 supergravity corresponding to M-theory compactified on a "barely" G2 manifold involving CY3(3, 243) and a conjecture related to the action of antiholomorphic involution on period integrals. We then shown an indirect connection between the two topics by showing a connection between each one of the two and Witten's MQCD.3 As an aside, we show that in the limit of vanishing "ζ", a complex constant that appears in the Riemann surfaces relevant to defining the boundary conditions for the domain wall in MQCD, the infinite series of Ref. 4 used to represent a suitable embedding of a supersymmetric 3-cycle in a G2-mannifold, can be summed.