Boundary $σ$-model and corrections to D-brane actions

Abstract

We consider a $σ$-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 $R_{ijkl}[Φ^i,Φ^j][Φ^k,Φ^l]$.