Linde problem in Yang-Mills theory compactified on R-2 x T-2

Abstract

We investigate the perturbative expansion in SU(3) Yang-Mills theory compactified on R-2 x T-2 where the compact space is a torus T-2 = S-beta(1) x S-L(1), with S-beta(1) being a thermal circle with period beta = 1/T (T is the temperature) while S-L(1) is a circle with finite length L = 1/M, where M is an energy scale. A Linde-type analysis indicates that perturbative calculations for the pressure in this theory break down already at order O(g(2)) due to the presence of a nonperturbative scale similar to g root TM. We conjecture that a similar result should hold if the torus is replaced by any other compact surface of genus one.