A note on the Supergravity Description of Dielectric Branes

TL;DR

This paper discusses supergravity solutions for dielectric branes, showing they correspond to known worldvolume theories and are likely the correct gravitational descriptions of such branes.

Contribution

It unifies recent supergravity solutions for dielectric branes and demonstrates their consistency with worldvolume theory predictions.

Findings

Supergravity solutions have two specific radii with the lower radius solution having lower energy.

The radii values match those predicted by D6-brane worldvolume theory.

The solutions are consistent with dielectric brane descriptions by Emparan and Myers.

Abstract

We comment on the recent papers by Costa et al and Emparan, which show how one might generate supergravity solutions describing certain dielectric branes in ten dimensions. The ``basic'' such solutions describe either N fundamental strings or N D4-branes expanding into a D6-brane, with topology M^2 x S^5 or M^5 x S^2 respectively. Treating these solutions in a unified way, we note that they allow for precisely two values of the radius of the relevant sphere, and that the solution with the smaller value of the radius has the lower energy. Moreover, the possible radii in both cases agree up to numerical factors with the corresponding solutions of the D6-brane worldvolume theory. We thus argue that these supergravity solutions are the correct gravitational description of the dielectric branes of Emparan and Myers.