RENORMALONS FROM 8-LOOP EXPANSION OF THE GLUON CONDENSATE IN LATTICE GAUGE-THEORY

In SU(3) lattice gauge theory in four dimensions we compute the first eight perturbative coefficients of the expectation value of the Wilson loop on the elementary plaquette which is related to the gluon conden sate. This result is obtained by using a numerical method recently pro posed, Only the first three coefficients have been computed analytical ly, The coefficients grow with the order. We show that this growth is related to the non-convergence of the perturbative expansion due to th e infrared renormalon associated to the gluon condensate. This conclus ion is based on assuming that the renormalon expansion is expressed in a continuum coupling (e.g. in the <(MS)over bar> scheme),taking into account the large perturbative corrections between the continuum and t he lattice coupling (up to three loops in <(MS)over bar>). To corrobor ate this conclusion we have computed, with less statistics, the first eight perturbative coefficients for the double plaquette. The coeffici ents for the elementary and double plaquette grow in a similar way and this is in agreement with the universality of the renormalon singular ity.