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.