Semilocal Fractional Instantons

TL;DR

This paper discovers semi-local fractional instantons in gauge theories and sigma models, revealing their properties, exact solutions, and dualities, with implications for understanding non-perturbative effects in supersymmetric theories.

Contribution

It introduces semi-local fractional instantons in gauge theories and sigma models, providing exact solutions and analyzing their dualities and charge properties.

Findings

Exact solutions for sigma model instantons are constructed.

Finite gauge coupling resolves small instanton singularities.

Instanton charges differ in Abelian and non-Abelian theories, related by duality.

Abstract

We find semi-local fractional instantons of codimension four in Abelian and non-Abelian gauge theories coupled with scalar fields and the corresponding ${\mathbb C}P^{N-1}$ and Grassmann sigma models at strong gauge coupling. They are 1/4 BPS states in supersymmetric theories with eight supercharges, carry fractional (half) instanton charges characterized by the fourth homotopy group $\pi_4 (G/H)$, and have divergent energy in infinite spaces. We construct exact solutions for the sigma models and numerical solutions for the gauge theories. Small instanton singularity in sigma models is resolved at finite gauge coupling (for the Abelian gauge theory). Instantons in Abelian and non-Abelian gauge theories have negative and positive instantons charges, respectively, which are related by the Seiberg-like duality that changes the sign of the instanton charge.