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

TL;DR

This paper investigates the fermionic interactions on a D3-brane within a supergravity background, revealing specific flux couplings, dipole moments, gauge invariance, and duality properties, with implications for N=1 supersymmetric gauge theories.

Contribution

It provides a detailed analysis of fermion-boson couplings in D3-brane actions, including flux interactions, gauge fixing independence, and SL(2,R) self-duality, in a supergravity context.

Findings

Coupling between fermions and 3-form flux is only through *G_3 - iG_3, which vanishes in certain solutions.

Fermions exhibit magnetic and electric dipole moments proportional to the dilaton-axion derivative.

Interaction terms are gauge-independent and SL(2,R) self-dual.

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.