Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice SO(Nc) gauge theories

TL;DR

This paper studies the low-temperature critical behavior of two-dimensional lattice SO(Nc) gauge theories with multicomponent scalar fields, revealing their universal features align with the RP(Nf-1) model class.

Contribution

It demonstrates that these gauge theories exhibit a universal low-temperature critical behavior akin to the RP(Nf-1) model, extending understanding of nonabelian gauge theories in two dimensions.

Findings

No finite-temperature symmetry breaking for Nf >= 3.

Correlation length grows exponentially at zero temperature.

Universal behavior matches the two-dimensional RP(Nf-1) model.

Abstract

We address the interplay between global and local gauge nonabelian symmetries in lattice gauge theories with multicomponent scalar fields. We consider two-dimensional lattice scalar nonabelian gauge theories with a local SO(Nc) (Nc >= 3) and a global O(Nf) invariance, obtained by partially gauging a maximally O(Nf x Nc)-symmetric multicomponent scalar model. Correspondingly, the scalar fields belong to the coset S(Nf Nc-1)/SO(Nc), where S(N) is the N-dimensional sphere. In agreement with the Mermin-Wagner theorem, these lattice SO(Nc) gauge models with Nf >= 3 do not have finite-temperature transitions related to the breaking of the global nonabelian O(Nf) symmetry. However, in the zero-temperature limit they show a critical behavior characterized by a correlation length that increases exponentially with the inverse temperature, similarly to nonlinear O(N) sigma models. Their universal features are investigated by numerical finite-size scaling methods. The results show that the asymptotic low-temperature behavior belongs to the universality class of the two-dimensional RP(Nf-1) model.