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

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.

30 pages, 13 figures; v2: minor changes; v3: minor changes

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• Critical Dimension and Negative Specific Heat in One-dimensional Large-N Reduced Models
• Simple non-perturbative resummation schemes beyond mean-field II: thermodynamics of scalar ${\varphi }^4$ theory in 1+1 dimensions at arbitrary coupling
• Real Time Quantum Gravity Dynamics from Classical Statistical Yang-Mills Simulations
• Exact $\beta$-function of Yang-Mills theory in 2+1 dimensions