Perturbative contributions to Wilson loops in twisted lattice boxes and reduced models

Abstract

We compute the perturbative expression of Wilson loops up to order $g^4$ for SU($N$) lattice gauge theories with Wilson action on a finite box with twisted boundary conditions. Our formulas are valid for any dimension and any irreducible twist. They contain as a special case that of the 4-dimensional Twisted Eguchi-Kawai model for a symmetric twist with flux $k$. Our results allow us to analyze the finite volume corrections as a function of the flux. In particular, one can quantify the approach to volume independence at large $N$ as a function of flux $k$. The contribution of fermion fields in the adjoint representation is also analyzed.

arXiv commentpdflatex 57 pages, 9 figures, 4 appendices

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• Bootstrap Method in Theoretical Physics
• The perturbative SU(N) one-loop running coupling in the twisted gradient flow scheme