Construction of exact Riemannian instanton solutions

TL;DR

This paper constructs exact Riemannian instanton solutions in 2d Yang-Mills theories, revealing their structure as condensates of solitons satisfying integrable equations, with implications for string configurations.

Contribution

It provides the first exact construction of Riemannian instantons satisfying Hitchin equations with boundary conditions, linking them to integrable soliton solutions in gauge theories.

Findings

Solutions are condensates of infinite solitons with identical topological charge.

The equations reduce to the sinh-Gordon equation with a delta source.

The method employs integrable theory techniques based on zero curvature conditions.

Abstract

We give the exact construction of Riemannian (or stringy) instantons, which are classical solutions of 2d Yang-Mills theories that interpolate between initial and final string configurations. They satisfy the Hitchin equations with special boundary conditions. For the case of U(2) gauge group those equations can be written as the sinh-Gordon equation with a delta function source. Using techniques of integrable theories based on the zero curvature conditions, we show that the solution is a condensate of an infinite number of one-solitons with the same topological charge and with all possible rapidities.