Dirac actions for D-branes on backgrounds with fluxes

TL;DR

This paper addresses the fermionic sector of D-brane world-volume actions in general flux backgrounds by deriving a simple Dirac-like form for the quadratic fermionic action applicable to any Dp-brane. The authors show that the world-volume fluxes deform the naive Dirac operator but these effects can be absorbed into a generalized kinetic term using a deformed world-volume metric M = g + F, enabling a canonical Dirac operator after a geometric redefinition. They establish T-duality consistency, provide a κ-fixed form, and construct a rotated, canonical action with explicit background couplings, clarifying how fluxes influence world-volume geometry and supersymmetry. The results offer a practical framework for calculations of nonperturbative effects and realistic D-brane model building in flux backgrounds.

Abstract

The understanding of the fermionic sector of the worldvolume D-brane dynamics on a general background with fluxes is crucial in several branches of string theory, like for example the study of nonperturbative effects or the construction of realistic models living on D-branes. In this paper we derive a new simple Dirac-like form for the bilinear fermionic action for any Dp-brane in any supergravity background, which generalizes the usual Dirac action valid in absence of fluxes. A nonzero world-volume field strength deforms the usual Dirac operator in the action to a generalized non-canonical one. We show how the canonical form can be re-established by a redefinition of the world-volume geometry.