D3 Brane Action and Fermion Zero Modes in Presence of Background Flux

TL;DR

The work addresses non-perturbative corrections to the IIB superpotential arising from Euclidean D3-brane instantons wrapping divisors in flux backgrounds. It develops a gauge-completion method to derive all fermion bilinear terms in the D3 worldvolume action by expanding IIB superfields to $O(\theta^2)$, then analyzes the resulting mass terms generated by background $H$- and $F'$-flux. A key finding is that three-form flux generically breaks the $U(1)$ symmetry associated with rotations in the normal plane to the divisor, altering zero-mode counting and enabling corrections beyond the unity-arithmetic-genus criterion in many cases. An explicit $T^6/\mathbb{Z}_2$ example demonstrates that flux lifts a subset of zero modes (six of sixteen), illustrating the mechanism's efficacy and guiding future computations of instanton-induced superpotential terms in flux vacua.

Abstract

We derive the fermion bilinear terms in the world volume action for a D3 brane in the presence of background flux. In six-dimensional compactifications non-perturbative corrections to the superpotential can arise from an Euclidean D3-brane instanton wrapping a divisor in the internal space. The bilinear terms give rise to fermion masses and are important in determining these corrections. We find that the three-form flux generically breaks a U(1) subgroup of the structure group of the normal bundle of the divisor. In an example of compactification on T^6/Z_2, six of the sixteen zero modes originally present are lifted by the flux.