Gauge Symmetry Enhancement and Radiatively Induced Mass in the Large N Nonlinear Sigma Model

TL;DR

This paper investigates a coupled nonlinear sigma model in 1+1 dimensions, revealing how gauge bosons gain radiative masses that vanish at self-dual points, indicating gauge symmetry enhancement and a preference for a non-Abelian fixed point.

Contribution

It introduces a hybrid model of coupled complex projective spaces, analyzing gauge symmetry enhancement and mass generation in the large N limit.

Findings

Gauge bosons acquire radiative masses that vanish at self-dual points.

Self-dual points correspond to Grassmann manifold target space.

The theory favors a non-Abelian ultraviolet fixed point.

Abstract

We consider a hybrid of nonlinear sigma models in which two complex projective spaces are coupled with each other under a duality. We study the large N effective action in 1+1 dimensions. We find that some of the dynamically generated gauge bosons acquire radiatively induced masses which, however, vanish along the self-dual points where the two couplings characterizing each complex projective space coincide. These points correspond to the target space of the Grassmann manifold along which the gauge symmetry is enhanced, and the theory favors the non-Abelian ultraviolet fixed point.