Instanton dynamics in the broken phase of the topological sigma model

The topological σ model with the black hole metric of the target space is considered. It has been shown before that this model is in the phase with BRST symmetry broken. In particular, the vacuum energy is nonzero and correlation functions of observables show the coordinate dependence. However, these quantities turn out to be infrared-divergent. It is shown here that IR divergences disappear after the sum over an arbitrary number of additional instanton-anti-instanton pairs is performed. The model appears to be equivalent to the Coulomb gas/sine-Gordon system.