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

摘要

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, nonuniform, and center-symmetric configurations as a function of the lattice coupling.