Oblate, Toroidal, and Other Shapes for the Enhancon

TL;DR

This paper investigates complex supergravity geometries with various shapes, including toroidal forms, created by wrapped D-branes, and explores their physical consistency and implications for gauge theories.

Contribution

It introduces new geometrical configurations involving multiple enhancon shells and tests their consistency using supergravity and brane techniques.

Findings

Two nested enhancon shells can merge into a toroidal surface.

Supergravity surgery confirms the physical consistency of the geometries.

Implications for the Coulomb branch of 2+1 dimensional SU(N) gauge theory are derived.

Abstract

We present some results of studying certain axially symmetric supergravity geometries corresponding to a distribution of BPS D6-branes wrapped on K3, obtained as extremal limits of a rotating solution. The geometry's unphysical regions resulting from the wrapping can be repaired by the enhancon mechanism, with the result that there are two nested enhancon shells. For a range of parameters, the two shells merge into a single toroidal surface. Given the quite intricate nature of the geometry, it is an interesting system in which to test previous techniques that have been brought to bear in spherically symmetric situations. We are able to check the consistency of the construction using supergravity surgery techniques, and probe brane results. Implications for the Coulomb branch of (2+1)-dimensional pure SU(N) gauge theory are extracted from the geometry. Related results for wrapped D4- and D5-brane distributions are also discussed.