Linde problem in Yang-Mills theory compactified on R2× T2

We investigate the perturbative expansion in SU(3) Yang-Mills theory compactified on R2×T2 where the compact space is a torus T2=Sβ1×SL1, with Sβ1 being a thermal circle with period β=1/T (T is the temperature) while SL1 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(g2) due to the presence of a nonperturbative scale ∼gTM. We conjecture that a similar result should hold if the torus is replaced by any other compact surface of genus one.