θ dependence of the deconfining phase transition in pure SU(Nc) Yang-Mills theories

Recently, it has been conjectured that deconfining phase transition in SU(N-c) pure Yang-Mills theories is continuously connected to a quantum phase transition in softly broken N = 1 super Yang-Mills on R-1,R-2 x S-1. We exploit this conjecture to study the strength of the transition and deconfining temperature as a function of the vacuum angle similar to in pure Yang- Mills. We find that the transition temperature is a decreasing function of theta is an element of inverted right perpendicular0, pi), in an excellent agreement with recent lattice simulations. We also predict that the transition becomes stronger for the same range of theta, and comment on the theta dependence in the large Nc limit. More lattice studies are required to test our predictions.