Non-Perturbative Effects on a Fractional D3-Brane

TL;DR

This work shows that non-perturbative effects from D-instantons can generate substantial superpotential and condensate structure in an otherwise abelian $U(1)$ worldvolume theory, provided gravity is not fully decoupled. By analyzing a local $\mathcal{N}=1$ brane setup on a $\mathbb{C}^3/\mathbb{Z}_2\times\mathbb{Z}_2$ orbifold, the authors derive ADS-like and polynomial instanton superpotentials for Cases A and B, and demonstrate explicit moduli-space integrals yielding $W^{\mathrm{np}}$ and gaugino condensates in the appropriate limits, including the pure $U(1)$ and pure $Sp(0)$ cases. They also extend the analysis to flux backgrounds, where $(0,3)$-flux enables instanton effects without gauge branes and $(3,0)$-flux introduces SUSY-breaking terms and flux-induced non-perturbative contributions to the cosmological constant and to non-supersymmetric mass terms. Collectively, the results illuminate how stringy UV completion, orientifold projections, and background fluxes conspire to give rise to non-perturbative dynamics in low-rank gauge theories, with implications for moduli stabilization and the structure of the 4d effective action in flux compactifications.

Abstract

In this note we study the N=1 abelian gauge theory on the world volume of a single fractional D3-brane. In the limit where gravitational interactions are not completely decoupled we find that a superpotential and a fermionic bilinear condensate are generated by a D-brane instanton effect. A related situation arises for an isolated cycle invariant under an orientifold projection, even in the absence of any gauge theory brane. Moreover, in presence of supersymmetry breaking background fluxes, such instanton configurations induce new couplings in the 4-dimensional effective action, including non-perturbative contributions to the cosmological constant and non-supersymmetric mass terms.