Lattice Simulations of 10d Yang-Mills toroidally compactified to 1d, 2d and 4d

TL;DR

This paper uses lattice simulations to study toroidally compactified Yang-Mills theories in various dimensions, confirming previous results and exploring phase structures and symmetry breaking phenomena.

Contribution

It provides new lattice simulation data for Yang-Mills theories in 1, 2, and 4 dimensions, including phase diagrams and eigenvalue distributions, extending understanding of their non-perturbative behavior.

Findings

Confirmed phase diagram in (1+1) dimensions.

Observed sequential center symmetry breaking in (1+1) dimensions.

Presented initial results on eigenvalue distributions in (3+1) dimensions.

Abstract

Toroidally compactified Yang-Mills theory on the lattice is studied by using the Hybrid Monte Carlo algorithm. When the compact dimensions are small, the theory naturally reduces to Yang-Mills with scalars. We confirm previous analytical and numerical results for pure gauge theory with scalars in (0+1) dimensions and at high temperatures to Super-Yang-Mills in (1+1) dimensions. In (1+1) dimensions, our simulations confirm the previously conjectured phase diagram. Furthermore, we find evidence for the sequential breaking of the center symmetry in (1+1) dimensions as a function of the volume. In (3+1) dimensions we present first simulation results for the eigenvalue distribution of the Polyakov and Wilson loops, finding localized, non-uniform and center-symmetric configurations as a function of the lattice coupling.