Aspects of membrane instanton calculations in strongly coupled string theories

We study non-perturbative effects in the strong coupling limit of Heterotic E8 x E8 string theory. Low energy limit of this theory potential reproduces the standard model of particle physics. Non-perturbative effects arise from membrane instantons wrapping certain submanifolds in the “Calabi-Yau x Horava-Witten interval”, which is a seven dimensional space used to compactify eleven dimensional M theory. We calculate superpotential in four dimensions by focusing on the vertex operators of chiral fermions. Corresponding potential leads to attractive as well as repulsive forces between M5 branes and the “end of the world branes”, depending on the region in the moduli space of heterotic M theory. The resulting dynamics on moduli space include a strong coupling dual to the Dine-Seiberg instability, in which the Horava-Witten interval grows to infinity. We consider one, as well as multiple M5 branes along the interval and show the emergence of Toda like potentials for the position moduli of M5 branes. We use M theory/type IIA duality to derive multicover formula for membrane instantons and study its effects on chirality changing phase transitions in heterotic M theory. We also explore the supersymmetric black hole solutions in gauged four dimensional supergravity.