The Broken Phase of the Topological Sigma model

TL;DR

This paper investigates the topological sigma model with a black hole-like target space, revealing the existence of unsuppressed instantons, multiple vacuum states, and broken BRST-symmetry, which lead to unusual physical phenomena.

Contribution

It demonstrates the presence of unsuppressed instantons and multiple vacua with broken BRST-symmetry in the topological sigma model with a semi-infinite cigar target space.

Findings

Existence of unsuppressed instantons due to noncompact moduli space

Identification of stable vacuum with zero energy and topological correlation functions

Discovery of other vacua with nonzero energy and coordinate-dependent correlators

Abstract

The topological sigma model with the semi-infinite cigar-like target space (black hole geometry) is considered. The model is shown to possess unsuppressed instantons. The noncompactness of the moduli space of these instantons is responsible for an unusual physics. There is a stable vacuum state in which the vacuum energy is zero, correlation functions are numbers thus the model is in the topological phase. However, there are other vacuum states in which correlation functions show the coordinate dependence. The estimation of the vacuum energy indicates that it is nonzero. These states are interpreted as the ones with broken BRST-symmetry.