Finite action solutions of SO(2,1) Hitchin's equations

TL;DR

This paper introduces a new family of finite action solutions to SO(2,1) Hitchin's equations, analyzes their properties, and extends them to multi-particle configurations, contributing to the understanding of these gauge-theoretic equations.

Contribution

It presents a one-parameter family of smooth finite action solutions to SO(2,1) Hitchin's equations and generalizes them to multi-particle solutions, which is a novel development.

Findings

Existence of a 1-parameter family of solutions

Solutions are smooth for fixed parameter values

Multi-particle generalizations of solutions

Abstract

We present a 1-parameter family of finite action solutions to the $S0(2,1)$ Hitchin's equations and explore some of its basic properties. For a fixed value of the parameter, the solution is smooth. We conclude by showing a multi-particle generalization of our basic solutions.