Actions and Fermionic symmetries for D-branes in bosonic backgrounds

TL;DR

This paper derives the complete interacting actions for supersymmetric D-branes in arbitrary bosonic backgrounds, revealing their symmetry properties and providing explicit transformation rules, with an example involving D4-branes in D0-brane backgrounds.

Contribution

It presents the full component form of D-brane actions up to second order in fermions in general backgrounds, including explicit symmetry transformations and an illustrative example.

Findings

Actions exhibit κ-symmetry and supersymmetry with Killing spinors.

Explicit transformation rules for symmetries are provided.

Example analysis of D4-brane in D0-brane background shows rigid supersymmetry.

Abstract

In this article we derive the full interacting effective actions for supersymmetric D-branes in arbitrary bosonic type II supergravity backgrounds. The actions are presented in terms of component fields up to second order in fermions. As one expects, the actions are built from the supercovariant derivative operator and the $\kappa$-symmetry projector. The results take a compact and elegant form exhibiting $\kappa$-symmetry, as well as supersymmetry in a background with Killing spinors. We give the explicit transformation rules for these symmetries in all cases, including the M2-brane. As an example, we analyze the N=2 super-worldvolume field theory defined by a test D4-brane in the supergravity background produced by a large number of D0-branes. This example displays rigid supersymmetry in a curved spacetime.