Monopoles and Instantons on Partially Compactified D-Branes

TL;DR

This paper explores monopoles and instantons in supersymmetric SU(N) Yang-Mills theory on a partially compactified space, revealing their moduli space structure and connections to Kronheimer's gauge theory, extending previous results to finite couplings.

Contribution

It explicitly constructs the monopole and instanton moduli space on $S^1 imes R^{3+1}$ and relates it to Coulomb phase moduli space of a 2+1 dimensional U(1)^N gauge theory, extending prior work.

Findings

Identifies N-1 fundamental monopoles and a KK monopole in the theory.

Shows the moduli space matches Coulomb phase of U(1)^N gauge theory.

Relates instanton solutions to Kronheimer's gauge theory of SU(N).

Abstract

Motivated by the recent D-brane constructions of world-volume monopoles and instantons, we study the supersymmetric SU(N) Yang-Mills theory on $S^1 \times R^{3+1}$, spontaneously broken by a Wilson loop. In addition to the usual N-1 fundamental monopoles, the N-th BPS monopole appears from the Kaluza-Klein sector. When all N monopoles are present, net magnetic charge vanishes and the solution can be reinterpreted as a Wilson-loop instanton of unit Pontryagin number. The instanton/multi-monopole moduli space is explicitly constructed, and seen to be identical to a Coulomb phase moduli space of a U(1)^N gauge theory in 2+1 dimensions related to Kronheimer's gauge theory of SU(N) type. This extends the results by Intriligator and Seiberg to the finite couplings that, in the infrared limit of Kronheimer's theory, the Coulomb phase parameterizes a centered SU(N) instanton. We also elaborate on the case of restored SU(N) symmetry.