Two-dimensional lattice SU($N_c$) gauge theories with multiflavor adjoint scalar fields

TL;DR

This paper investigates two-dimensional lattice SU(N_c) gauge theories with multiple adjoint scalar fields, analyzing conditions for a continuum limit and its relation to sigma models on symmetric spaces, extending previous theoretical insights.

Contribution

It extends prior work by examining the influence of gauge-group representation and scalar potential on the continuum limit in multiflavor adjoint scalar lattice gauge theories.

Findings

Continuum limit exists under specific conditions.

Continuum limit corresponds to sigma models on symmetric spaces.

Results support the conjecture linking lattice models to symmetric space sigma models.

Abstract

We consider two-dimensional lattice SU($N_c$) gauge theories with $N_f$ real scalar fields transforming in the adjoint representation of the gauge group and with a global O($N_f$) invariance. Focusing on systems with $N_f\ge 3$, we study their zero-temperature limit, to understand under which conditions a continuum limit exists, and to investigate the nature of the associated quantum field theory. Extending previous analyses, we address the role that the gauge-group representation and the quartic scalar potential play in determining the nature of the continuum limit (when it exists). Our results further corroborate the conjecture that the continuum limit of two-dimensional lattice gauge models with multiflavor scalar fields, when it exists, is associated with a $\sigma$ model defined on a symmetric space that has the same global symmetry as the lattice model.