Weak coupling perturbative calculations of the Wilson loop for the standard action

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

“…In the previous formulas we have added a third column corresponding to the infinite volume limit. It reproduces the results of Weisz, Wetzel and Wohlert [11] for the four dimensional case.…”

“…We also add the coefficient K(R, R) used in ref. [11]. Our calculations are consistent with the precise results of ref.…”

“…As mentioned in the introduction, this problem has been addressed earlier by several authors [7][8][9][10][11][12]. The main difference of our work with others is that we will consider arbitrary orthogonal irreducible twisted boundary conditions on the lattice [13,59].…”

“…[9][10][11], we arrive at the following expression for the coefficients of the logarithm of the Wilson loop at O(g 4 ):…”

“…Other studies simply ignored the problem by expanding around a single type of minima [7]. The results should approach those obtained at infinite volume [8][9][10][11][12]. 1 't Hooft realized that PBC are not the only possible boundary conditions for SU(N) gauge theories on the torus.…”