Exact Results in Gluodynamics: Topological Susceptibility, Condensates and Θ Dependence

We derive a series of low energy theorems for correlation functions of the topological density in gluodynamics. In particular, the topological susceptibility is found exactly in terms of the gluon condensate. Using low energy theorems, we find the θ dependence of the condensates 〈GG〉, 〈GG̃〉 and of the partition function for small θ and an arbitrary number of colors. As applications of low energy theorems, we find the value of the gluon condensate in gluodynamics from the Witten-Veneziano formula and calculate quantum correlations between the self-dual and anti-self-dual sectors of the theory.