Dielectric-Branes

TL;DR

This paper develops a nonabelian generalization of D-brane world-volume actions by enforcing T-duality, yielding a U(N) gauge theory on the brane with new commutator terms and couplings to RR potentials of all degrees. It demonstrates that external fields can polarize branes into higher-dimensional, noncommutative configurations, exemplified by D0-branes expanding into a spherical D2 bound state in a RR four-form background. The framework combines a nonabelian Born-Infeld action with a generalized Chern-Simons action, and a symmetrized trace prescription is used to align with Matrix Theory results, providing explicit checks for linear couplings and a D0–D2 dual description. The work also discusses limitations and future directions, including supersymmetric completion and higher-order corrections, with implications for dielectric brane physics and noncommutative geometry.

Abstract

We extend the usual world-volume action for a Dp-brane to the case of N coincident Dp-branes where the world-volume theory involves a U(N) gauge theory. The guiding principle in our construction is that the action should be consistent with the familiar rules of T-duality. The resulting action involves a variety of potential terms, i.e., nonderivative interactions, for the nonabelian scalar fields. This action also shows that Dp-branes naturally couple to RR potentials of all form degrees, including both larger and smaller than p+1. We consider the dynamics resulting from this action for Dp-branes moving in nontrivial background fields, and illustrate how the Dp-branes are ``polarized'' by external fields. In a simple example, we show that a system of D0-branes in an external RR four-form field expands into a noncommutative two-sphere, which is interpreted as the formation of a spherical D2-D0 bound state.