Fractional instantons and Confinement: first results on a $T_2\times R^2$ roadmap

TL;DR

This paper investigates SU(2) Yang-Mills theory on a four-dimensional torus with two small directions, revealing how fractional instantons influence topological charge and confinement, bridging semiclassical and infinite-volume regimes.

Contribution

It provides the first numerical evidence linking fractional instantons to confinement phenomena in a controlled torus setup with twisted boundary conditions.

Findings

Fractional instantons contribute to topological charge and string tension.

Density of fractional instantons increases with torus size.

Results support the fractional instanton liquid model of the Yang-Mills vacuum.

Abstract

We report results obtained for SU(2) Yang-Mills theory on a four dimensional torus with two directions much smaller than the other two. The small 2-torus is equipped with twisted boundary conditions. This construction provides a way to interpolate from a region in which semiclassical methods can be applied (for small 2-torus size) to the standard infinite volume case. Our simulations at small torus sizes show how the topological charge and the string tension result from a gas of vortex-like fractional instantons. As the size becomes larger the density increases and the separation of structures tends to a constant in agreement with the fractional instanton liquid model picture of the Yang-Mills vacuum.