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

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.

Comments: 15 pages, 9 figures. Contribution for the Proceedings of the 41st International Symposium on Lattice Field Theory (Lattice 2024), 28 July-3 August 2024, Liverpool, UK