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

TL;DR

This paper derives fermion bilinear terms for a D3 brane with background flux, showing how flux influences fermion zero modes and non-perturbative superpotential corrections in string compactifications.

Contribution

It provides the explicit form of fermion bilinear terms in the D3 brane action in flux backgrounds, highlighting flux-induced lifting of zero modes.

Findings

Flux breaks a U(1) subgroup of the normal bundle structure group.

Six of sixteen fermion zero modes are lifted by flux in a T^6/Z_2 compactification.

Fermion bilinear terms are crucial for understanding non-perturbative effects.

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.