Topology in the Bulk: Gauge Field Solitons in Extra Dimensions

TL;DR

This paper explores gauge field solitons in 4+1 dimensions, revealing their topological nature, their relation to instantons and monopoles, and their implications for D-brane boundary conditions and monopole emissions.

Contribution

It introduces a novel interpretation of instantons as monopole exchanges in higher dimensions and connects topological gauge configurations with D-brane physics.

Findings

Static gauge field solitons correspond to higher-dimensional instantons.

Periodic instantons can be used to construct solutions satisfying D-brane boundary conditions.

The $ heta$-term acts as a topological current source, enabling monopole emission into the bulk.

Abstract

Certain static soliton configurations of gauge fields in 4+1 dimensions correspond to the instanton in 4-Euclidean dimensions ``turned on its side,'' becoming a monopole in 4+1. The periodic instanton solution can be used with the method of images to construct solutions satisfying D-brane boundary conditions. The $\theta$-term on the brane becomes a topological current source, yielding an emission amplitude for monopoles into the bulk. Instantons have a novel reinterpretation in terms of monopole exchange between branes.