MQCD, ('Barely') G_2 Manifolds and (Orientifold of) a Compact Calabi-Yau

Details MQCD, ('Barely') G_2 Manifolds and (Orientifold of) a Compact Calabi-Yau MQCD, ('Barely') G_2 Manifolds and (Orientifold of) a Compact Calabi-Yau

2004-02-29

arxiv.org/abs/hep-th/0403012v1

Int.J.Mod.Phys. A20 (2005) 2059-2098

Physics

High Energy Physics

High Energy Physics - Theory

37 pages, LaTex; PARTLY based on talks given at ``Seventh Workshop on QCD" [session on "Strings, Branes and (De-)Construction"

Scientific paper

10.1142/S0217751X05021075

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 G_2-manifold evaluated by the path-integral inside a path-integral approach of [1], and the other centered around the compact Calabi-Yau CY_3(3,243) expressed as a blow-up of a degree-24 Fermat hypersurface in WCP^4[1,1,2,8,12]. For the former, we compare the results with the ones of Witten on heterotic world-sheet instantons [2]. The subtopics covered in the latter include an N=1 triality between Heterotic, M- and F-theories, evaluation of RP^2-instanton superpotential, Picard-Fuchs equation for the mirror Landau-Ginsburg model corresponding to CY_3(3,243), D=11 supergravity corresponding to M-theory compactified on a `barely' G_2 manifold involving CY_3(3,243) and a conjecture related to the action of antiholomorphic involution on period integrals. We then show 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 "\zeta", a complex constant that appears in the Riemann surfaces relevant to definining the boundary conditions for the domain wall in MQCD, the infinite series of [4] used to represent a suitable embedding of a supersymmetric 3-cycle in a G_2-mannifold, can be summed.

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