Non-Perturbative Superpotentials from Membrane Instantons in Heterotic M-Theory

TL;DR

This work addresses non-perturbative moduli stabilization in heterotic M-theory by computing open membrane instanton contributions to the four-dimensional superpotential $W$ arising from membranes stretched between the orbifold boundary branes. The authors develop a κ-invariant open-membrane action with boundary $E_8$ gauge coupling via a boundary chiral Wess-Zumino-Witten model and show that BPS configurations require the membrane to end on holomorphic curves in a Calabi–Yau threefold, with a small interval limit yielding the heterotic string. They extract a concrete expression for the non-perturbative $W$ by evaluating the fermion two-point function and matching it to the 4D effective action, finding $W$ proportional to determinants of Dirac operators and boundary WZW determinants multiplied by an exponential factor $e^{-rac{T}{2}\sum_I \omega_I T^I}$; crucially, $W$ vanishes unless the pullback of the boundary bundles to the curve is trivial. The results illuminate a calculable mechanism for moduli stabilization in realistic heterotic vacua and set the stage for further extensions to multi-instanton and boundary-bulk superpotential contributions.

Abstract

A formalism for calculating the open supermembrane contribution to the non-perturbative superpotential of moduli in heterotic M-theory is presented. This is explicitly applied to the Calabi-Yau (1,1)-moduli and the separation modulus of the end-of-the-world BPS three-branes, whose non-perturbative superpotential is computed. The role of gauge bundles on the boundaries of the open supermembranes is discussed in detail, and a topological criterion presented for the associated superpotential to be non-vanishing.