An index for the Dirac operator on D3 branes with background fluxes

TL;DR

This paper develops an index to determine when D3 brane instantons can generate superpotentials in type IIB string compactifications with fluxes, providing a tool for analyzing non-perturbative effects.

Contribution

It introduces a novel index based on the Dirac operator on D3 branes that predicts superpotential generation in flux backgrounds, extending previous duality-based analyses.

Findings

The index correctly predicts superpotential generation in various examples.

Results are consistent with duality and M-theory analyses.

The formalism applies to fluxed and fluxless compactifications.

Abstract

We study the problem of instanton generated superpotentials in Calabi-Yau orientifold compactifications directly in type IIB string theory. To this end, we derive the Dirac equation on a Euclidean D3 brane in the presence of background fluxes. We propose an index which governs whether the generation of a superpotential in the effective 4d theory by D3 brane instantons is possible. Applying the formalism to various classes of examples, including the K3 x T^2/Z_2 orientifold, in the absence and presence of fluxes, we show that our results are consistent with conclusions attainable via duality from an M-theory analysis.