Fermions, T-duality and effective actions for D-branes in bosonic backgrounds

TL;DR

This work provides the first explicit, covariant, component-field formulation of Dp-brane actions in general bosonic supergravity backgrounds up to second order in fermions, neglecting fermion–f interactions with $f=b+F$. The authors start from the M2-brane action, perform a normal-coordinate expansion, and reduce to the D2-brane, then generate all Dp-brane actions via T-duality using Hassan's formalism. The resulting actions combine a standard bosonic DBI–WZ sector with a quadratic fermionic term projected by $P^{Dp}_{(-)}$, and are constructed to be kappa-symmetric and duality-covariant to this order. A thorough set of background, spinor, and pull-back transformation rules is provided (with explicit formulas in the appendices), enabling covariant calculations in generic bosonic backgrounds and future work to incorporate the neglected $f$–fermion interactions and a detailed kappa-symmetry analysis.

Abstract

We find the effective action for any D-brane in a general bosonic background of supergravity. The results are explicit in component fields up to second order in the fermions and are obtained in a covariant manner. No interaction terms between fermions and the field $f=b+F$, characteristic of the bosonic actions, are considered. These are reserved for future work. In order to obtain the actions, we reduce directly from the M2-brane world-volume action to the D2-brane world-volume action. Then, by means of T-duality, we obtain the other Dp-brane actions. The resulting Dp-brane actions can be written in a single compact and elegant expression.