Five-Brane Superpotentials in Heterotic M-Theory

TL;DR

The paper computes a nonperturbative superpotential in heterotic M-theory arising from open membranes stretching between a boundary plane and a bulk five-brane. By performing a detailed κ-invariant construction, reducing to the heterotic string on a holomorphic curve, and evaluating the fermionic two-point function via a saddle-point expansion, it derives an explicit exponential suppression e^{−(T/2)𝔜} multiplied by determinants from bosonic, fermionic, and E8 boundary sectors. A key result is that the superpotential is holomorphic in the composite modulus 𝔜, built from the five-brane translation Y, the (1,1) modulus 𝒯 of the wrapped curve, and an axion, and it vanishes unless the boundary vector bundle restricts trivially to the curve. This provides a concrete mechanism for nonperturbative moduli stabilization and illuminates the role of boundary gauge bundles in controlling open-membrane instanton effects in heterotic M-theory.

Abstract

The open supermembrane contribution to the non-perturbative superpotential of bulk space five-branes in heterotic M-theory is presented. We explicitly compute the superpotential for the modulus associated with the separation of a bulk five-brane from an end-of-the-world three-brane. The gauge and kappa-invariant boundary strings of such open supermembranes are given and the role of the holomorphic vector bundle on the orbifold fixed plane boundary is discussed in detail.