The Compactified Principal Chiral Model's Mass Gap

TL;DR

This paper investigates how the topology of the vacuum manifold in compactified 2D sigma models influences the nonperturbative generation of a mass gap, revealing different behaviors based on boundary conditions and symmetry groups.

Contribution

It demonstrates that the connectedness of the vacuum manifold determines whether the mass gap is generated perturbatively or nonperturbatively in compactified sigma models.

Findings

SO(3) model has a disconnected vacuum manifold and a nonperturbative mass gap.

SU(2) principal chiral model has a connected vacuum manifold and a perturbative mass gap.

Topology of the vacuum manifold influences mass gap generation in 2D quantum field theories.

Abstract

If the space of minima of the effective potential of a weakly coupled 2d quantum field theory is not connected, then a mass gap will be nonpertubatively generated. As examples, we consider two sigma models compactified on a small circle with twisted boundary conditions. In the compactified SO(3) model the vacuum manifold consists of two points and the mass gap is nonperturbative. In the case of the compactified SU(2) principal chiral model the vacuum manifold is a single circle and the mass gap is perturbative.