The Linde problem on R2 x S1 x S1

Thermal field theory provides the natural framework to describe the thermodynamic properties and to study phase transitions of systems described by quantum field theories, in particular, the quark-gluon plasma. However, its the perturbative realization faces important technical difficulties whenever massless bosons are considered, due to divergences in the IR sector.

After briefly reviewing these IR divergences in thermal field theory, and especially the Linde problem, we analyze the IR behavior of Yang-Mills theory in a Torus -- R² x S¹ x S¹ -- and show that, in this geometry, any perturbative calculation is expected to break-down already at O(g²).