(Non-)BPS bound states and D-brane instantons

TL;DR

The paper addresses non-perturbative corrections to the four-dimensional ${\cal N}=1$ superpotential arising from D-brane instantons that are not orientifold-invariant. It shows that superpotential terms can be generated by multi-instanton recombinations at threshold, where a $U(1)$ instanton and two ${\rm O}(1)$ instantons lift all extra zero modes and form BPS bound states that either persist or decay as one moves across lines of marginal stability ${\cal M}_0$, ${\cal M}_+$, ${\cal M}_-$. The authors provide explicit realizations in Type IIA via Euclidean D2-instantons and in Type I via Euclidean D5-branes with holomorphic bundles, including a local toroidal example and the corresponding Type I mirror. They show that holomorphicity of the generated superpotential is preserved across transitions by matching contributions from different bound-state configurations, implying a broader class of instantons can correct the superpotential and suggesting a quantum deformation of the BPS spectrum in string compactifications.

Abstract

We study non-perturbative effects in four-dimensional N=1 supersymmetric orientifold compactifications due to D-brane instantons which are generically not invariant under the orientifold projection. We show that they can yield superpotential contributions via a multi-instanton process at threshold. Some constituents of this configuration form bound states away from the wall of marginal stability which can decay in other regions of moduli space. A microscopic analysis reveals how contributions to the superpotential are possible when new BPS states compensate for their decay. We study this concretely for D2-brane instantons along decaying special Lagrangians in Type IIA and for D5-branes instantons carrying holomorphic bundles in Type I theory.

Figures (2)

• Figure 1: Multi-instanton configuration involving two O(1) instantons.
• Figure 2: Multi-instanton configuration involving a single O(1) instanton.