Aspects of D-brane Dynamics in Supergravity Backgrounds with Fluxes, Kappa-symmetry and Equations of Motion. Part IIB

TL;DR

This paper derives detailed equations of motion for type IIB D-branes in supergravity backgrounds with fluxes, emphasizing fermionic modes and worldvolume gauge fields, with explicit forms for various Dp branes and examples involving non-zero fluxes.

Contribution

It provides explicit worldvolume field equations for Dp branes in flux backgrounds, including cases with non-zero Born-Infeld flux, and analyzes fermionic structures in these settings.

Findings

Explicit equations for Dp branes with zero flux

Examples of D3, D5, D7 branes with non-zero flux

Analysis of fermionic modes and Dirac equations

Abstract

We derive and carry out a detailed analysis of the equations of motion of the type IIB D branes in generic supergravity backgrounds with fluxes making account of the worldvolume Born-Infeld gauge field and putting a special emphasis on the structure of the Dirac equation for Dp brane fermionic modes. We present an explicit form of the worldvolume field equations for each of the Dp branes (p=1,3,5,7,9) in the cases in which the Neveu-Schwarz flux and the Ramond-Ramond p-form flux along the Dp-brane worldvolume are zero and the supergravity backgrounds do not necessarily induce the worldvolume Born-Infeld flux. We then give several examples of D3, D5 and D7 brane configurations in which the worldvolume Born-Infeld flux is intrinsically non-zero and therefore must be taken into account in studying problems where such branes are involved. The examples include D3 and D5 brane instantons carrying (self-dual) worldvolume gauge fields in warped compactification backgrounds.