Nonperturbative effects of Topological Theta-term

TL;DR

This paper investigates how a topological Theta-term influences the phase structure of 2+1D principal chiral models, revealing that at Theta = pi, the system can be either gapless or gapped with degeneracy, impacting boundary state analysis of 3D SPT phases.

Contribution

It provides a nonperturbative analysis of the effects of the Theta-term on principal chiral models, highlighting phase transitions at Theta = pi and applications to topological phases.

Findings

At Theta = pi, the model is either a gapless conformal field theory or gapped with degeneracy.

The topological Theta-term significantly alters the disordered phase of the model.

Results aid in understanding boundary states of 3D symmetry protected topological phases.

Abstract

We study the effects of a topological Theta-term on 2+1 dimensional principal chiral models (PCM), which are nonlinear sigma models defined on Lie group manifolds. We find that when Theta = pi, the nature of the disordered phase of the principal chiral model is strongly affected by the topological term: it is either a gapless conformal field theory, or it is gapped and two-fold degenerate. The result of our paper can be used to analyze the boundary states of three dimensional symmetry protected topological phases.