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

Understand

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.