Linde problem in Yang-Mills theory compactified on $\mathbb{R}^2 \times   \mathbb{T}^2$
  We investigate the perturbative expansion in $SU(3)$ Yang-Mills theory compactified on $\mathbb{R}^2\times \mathbb{T}^2$ where the compact space is a torus $\mathbb{T}^2= S^1_{\beta}\times S^1_{L}$, with $S^1_{\beta}$ being a thermal circle with period $\beta=1/T$ ($T$ is the temperature) while $S^1_L$ 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 $\mathcal{O}(g^2)$ due to the presence of a non-perturbative scale $\sim g \sqrt{TM}$. We conjecture that a similar result should hold if the torus is replaced by any other compact surface of genus one. 
Eduardo S. Fraga (Rio de Janeiro Federal U.), Daniel Kroff (Sao Paulo,   IFT), and Jorge Noronha (Sao Paulo U.)
hep-th hep-lat hep-ph