D3-brane action in a supergravity background: the fermionic story

TL;DR

This work derives the explicit coupling of D3-brane world-volume fermions to bosonic type IIB backgrounds preserving 4D Lorentz invariance, to second order in fermions. The renormalizable interactions arise exclusively through the complex 3-form flux as the combination $*_6 G_{(3)}-i G_{(3)}$, with gaugino and matter-fermion masses linked to the (3,0) and (1,2) components of $G_{(3)}$, respectively, and dipole moments tied to derivatives of the dilaton-axion $\tau$. The authors obtain the interaction Lagrangian via three routes: 10D covariance with gauge completion, ${\mathcal N}=1$ supersymmetry perturbations, and κ-symmetric D3-brane action, all of which agree and are checked against T-duality from D0-branes. The 4D interpretation places these couplings within ${\mathcal N}=1$ gauge theory language, linking brane-world phenomenology to F- and D-term SUSY breaking, and shows the action is gauge invariant and $SL(2,\mathbb{R})$ self-dual. The results illuminate how background fluxes shape the fermionic sector on D3-branes and provide a bridge to realistic brane constructions with fluxes.

Abstract

Using the kappa-symmetric action for a D3-brane, we study the interaction between its world-volume fermions and a bosonic type IIB supergravity background preserving 4-dimensional Lorentz invariance. We find that the renormalizable terms in the action include only coupling between the fermions and the 3-form flux in the combination *G_3-iG_3, which is zero for a class of supersymmetric and nonsupersymmetric solutions. We also find the magnetic and electric dipole moments for the fermions, which are proportional to the derivative of the dilaton-axion. We show that different gauges to fix the kappa-symmetry give the same interaction terms, and prove that these terms are also SL(2,R) self-dual. We interpret our results in terms of N=1 supersymmetric gauge theory on the D-brane.