Instanton Dynamics in the Broken Phase of the Topological Sigma Model

TL;DR

This paper investigates the instanton dynamics in a topological sigma model with broken BRST symmetry, showing how IR divergences are resolved through instanton-anti-instanton summation, revealing an equivalence to Coulomb gas/Sine Gordon systems.

Contribution

It demonstrates the IR divergence cancellation in the broken phase of the topological sigma model via instanton-anti-instanton sums and establishes its equivalence to Coulomb gas/Sine Gordon systems.

Findings

IR divergences are eliminated after summing over instanton-anti-instanton pairs

The model is equivalent to Coulomb gas/Sine Gordon system

Broken BRST symmetry leads to non-zero vacuum energy and coordinate-dependent correlators

Abstract

The topological $\sigma$ 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, vacuum energy is non-\-zero and correlation functions of observables show the coordinate dependence. However these quantities turned out to be infrared (IR) 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 Coulomb gas/Sine Gordon system.