Sheets of BPS Monopoles and Instantons with Arbitrary Simple Gauge Group

TL;DR

This paper demonstrates that BPS configurations with uniform field strength can be viewed as sheets of monopoles and instantons, revealing their zero mode structure and brane interpretations, thus deepening understanding of gauge theory solitons.

Contribution

It introduces a novel interpretation of BPS configurations as monopole and instanton sheets and analyzes their zero modes and brane realizations.

Findings

Number of zero modes per monopole charge is four.

Monopole sheets correspond to intersecting D3 branes.

Zero mode count for instantons matches that of isolated instantons.

Abstract

We show that the BPS configurations of uniform field strength can be interpreted as those for sheets of infinite number of BPS magnetic monopoles, and found that the number of normalizable zero modes per each magnetic monopole charge is four. We identify monopole sheets as the intersecting planes of D3 branes. Similar analysis on self-dual instanton configurations is worked out and the number of zero modes per each instanton number is found to match that of single isolated instanton.