Matrix Sigma-models for Multi D-brane Dynamics

TL;DR

This paper derives the low-energy effective action for multiple D-branes from a worldsheet sigma-model perspective, revealing the matrix-valued couplings and noncommutative geometry inherent in their dynamics.

Contribution

It provides a worldsheet derivation of the non-abelian D-brane effective action, connecting sigma-model couplings to matrix-valued collective coordinates.

Findings

Matrix couplings arise naturally from the worldsheet sigma-model.

Quantum dynamics enforce noncommutativity of the couplings.

Effective action matches the non-abelian Born-Infeld theory.

Abstract

We describe a dynamical worldsheet origin for the Lagrangian describing the low-energy dynamics of a system of parallel D-branes. We show how matrix-valued collective coordinate fields for the D-branes naturally arise as couplings of a worldsheet sigma-model, and that the quantum dynamics require that these couplings be mutually noncommutative. We show that the low-energy effective action for the sigma-model couplings describes the propagation of an open string in the background of the multiple D-brane configuration, in which all string interactions between the constituent branes are integrated out and the genus expansion is taken into account, with a matrix-valued coupling. The effective field theory is governed by the non-abelian Born-Infeld target space action which leads to the standard one for D-brane field theory.