Nuclear Physics B262 (1985) 67-94 © North-Holland Publishing Company ZERO-MOMENTUM CONTRIBUTION TO WILSON LOOPS IN PERIODIC BOXES A. COSTE*,A. GONZALEZ-ARROYO**, J. JURKIEWICZ*** and C.P. KORTHALS ALTES Centre de Physique Thborique,**** CNRS, Luminy, Case 907, F 13288, Marseille, France Received 6 June 1985 We compute the zero-momentumfinite-size effects in non-abelian gauge theories. In some cases, these effects are to lowest-order identical for lattice and continuum theories and are of the order of a few percent for an SU(3) gauge theory in four dimensions. 1. Introduction The measurement of Wilson loops in lattice gauge theories [1] by Monte Carlo methods [2] is subject to finite-size effects. Usually, measurements are performed on a finite lattice with periodic boundary conditions. This periodicity implies that in the strong coupling regime the finite-size effects are exponentially small as the linear size of the lattice grows in all directions. Eguchi and Kawai [3] observed that in strong coupling all finite-size effects are of order 1/N for gauge groups SU(N). Thus large-N theories do not feel the finite size of the system at least in strong coupling. In weak coupling, the situation is quite different. First of all the corrections are power behaved. Secondly they do not disappear for large-N except in two dimen- sions. The problem with these corrections is the following: the saddle points around which we study the fluctuations in perturbation theory are not only degenerate through gauge transformations, but there is an extra degeneracy due to the global toroidal structure of the periodic lattice [4]. Although equivalent on the classical level these saddle points or "torons" are no more equivalent on the quantum level: around some only gaussian fluctuations are present, around others a new type of fluctuations give rise to different power laws in the coupling. This is the qualitative * CPT--Marseille, Allocataire sur contrat n184/836, DRET/I~cole Polytechnique. ** Departamento de Fisica Teorica, mod. C-11, Universidad Autonoma de Madrid, Canto Blanco, Madrid, Spain. Universit6 d'Aix-Marseille II. ***Insituut theoretische fysica, Princetonplein, Rijks Universiteit Utrecht, De Uithof, Utrecht, The Netherlands. **** Laboratoire Propre CNRS. 67