Enhancons, Fuzzy Spheres and Multi-Monopoles

Abstract

We study the `enhancon', a spherical hypersurface apparently made of D-branes, which arises in string theory studies of large N SU(N) pure gauge theories with eight supercharges. When the gauge theory is 2+1 dimensional, the enhancon is an S^2. A relation to charge N BPS multi-monopoles is exploited to uncover many of its detailed properties. It is simply a spherical slice through an Atiyah-Hitchin-like submanifold of the charge $N$ BPS monopole moduli space. In the form of Nahm data, it is built from the N dimensional irreducible representation of SU(2). In this sense the enhancon is a non-commutative sphere, reminiscent of the spherical `dielectric' branes of Myers.

Figures (3)

• Figure 1: A summary of the geometry uncovered. There are three spheres shown: The unphysical repulson (innermost) was seen to be removed in ref.jpp, and replaced by the enhançon (next). Here, we find that the true non--perturbative enhançon radius is slightly different from this (shown outermost), although the correction is exponentially small at large $N$. The enhançon is a non--commutative sphere. There is smooth matching onto the spherically symmetric supergravity solution at large $N$. The region interior to the enhançon is the core of an $(N{-}1)$--monopole. There is an unbroken $SU(2)$ there.
• Figure 2: (a) The configuration of D3--branes stretching between NS5--branes. (b) The resulting "double trumpet" shape of the NS5--branes at large $N$. (A separated probe is also shown.) This system has a natural description in terms of the Nahm equations as explained in the text. The enhançon is the place (an $S^2$) where the NS5--branes touch.
• Figure 3: A plot of a slice of the two NS5--branes' shape, as deduced from the Higgs field (\ref{['one']}) for the single monopole. It is the only exactly spherically symmetric case. The double trumpet shape pinches off to zero size in this case.