Boundary $\sigma$-model and corrections to D-brane actions

TL;DR

This paper investigates the effects of gravitational corrections on D-brane actions within open string theory, using two-loop sigma-model calculations to analyze curvature couplings in curved backgrounds.

Contribution

It provides a two-loop analysis of gravitational corrections to D-brane actions, including new couplings involving curvature and scalar fields in curved ambient spaces.

Findings

Derived corrections to the Born-Infeld action in curved backgrounds

Identified specific curvature couplings for coincident D-branes

Extended understanding of D-brane dynamics in curved spacetime

Abstract

We consider a $\sigma$-model formulation of open string theory in the presence of D-branes. We perform two-loop computations and discuss gravitational corrections to Born-Infeld action when branes are non-trivially embedded in a curved ambient space. In particular for the case of a stack of $N$ coincident D-branes we analyze couplings of the form $R_{ijkl}[\Phi^i,\Phi^j][\Phi^k,\Phi^l]$.