The Enhancon, Multimonopoles and Fuzzy Geometry

TL;DR

This paper explores the enhancon geometry from wrapped D6-branes, relating it to multi-monopoles and fuzzy spheres, providing insights into non-perturbative string geometry and gauge theory moduli spaces.

Contribution

It uncovers the structure of the enhancon's moduli space, connects it to multi-monopoles, and introduces a fuzzy sphere description using Nahm data, advancing understanding of non-perturbative string geometries.

Findings

Enhanced understanding of the enhancon's non-perturbative geometry

Characterization of moduli space via Atiyah-Hitchin-like manifolds

Description of the enhancon locus as a fuzzy sphere

Abstract

The presentation at Strings 2000 was intended to be in two main parts, but there was only time for part one. However both parts appeared on the online proceedings, and are also included in this document. The first part concerns an exploration of the connection between the physics of the `enhancon' geometry arising from wrapping N D6-branes on the K3 manifold in Type IIA string theory and that of a charge N BPS multi-monopole. This also relates to the physics of 2+1 dimensional SU(N) gauge theory with eight supercharges. The main results uncovered by this exploration are: a) better insight into the non-perturbative geometry of the enhancon; b) the structure of the moduli space geometry, and its characterisation in terms of generalisations of an Atiyah-Hitchin-like manifold; c) the use of Nahm data to describe aspects of the geometry, showing that the enhancon locus itself has a description as a fuzzy sphere. Part two discusses the addition of extra D2-branes into the geometry. Two probe computations show the difference between the geometry as seen by D2-branes and that seen by wrapped D6-branes, and the accompanying gauge theory interpretations are discussed.