# The volume of a vortex and the Bradlow bound

## TL;DR

This paper shows that the geometric volume of vortices in certain field theories matches their thermodynamical volume, providing insights into bounds for vortex existence in various gauge theories.

## Contribution

It establishes the equivalence of geometric and thermodynamical volumes for vortices in higher-dimensional vacuum manifolds and relates this to Bradlow bounds in abelian gauge theories.

## Key findings

- Geometric volume coincides with thermodynamical volume for vortices.
- Bradlow bounds are applicable to a wide class of abelian gauge theories.
- In SDiff BPS models, vortex volume equals the Bradlow volume, which can be finite or infinite.

## Abstract

We demonstrate that the geometric volume of a soliton coincides with the thermodynamical volume also for field theories with higher-dimensional vacuum manifolds (e.g., for gauged scalar field theories supporting vortices or monopoles). We apply this observation to understand Bradlow type bounds for general abelian gauge theories supporting vortices. In the case of SDiff BPS models (being examples of perfect fluid models) we show that the geometric "volume" (area) of the vortex, which is base-space independent, is exactly equal to the Bradlow volume (a minimal volume for which a BPS soliton solution exists). This can be finite for compactons or infinite for infinitely extended solitons (in flat Minkowski space-time).