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

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.

arXiv comment8 pages. arXiv admin note: text overlap with arXiv:2001.07386

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• Critical points in the $R{P}^{N-1}$ model
• Two-dimensional lattice SU($N_c$) gauge theories with multiflavor adjoint scalar fields
• Berezinskii-Kosterlitz-Thouless transitions in two-dimensional lattice SO($N_c$) gauge theories with two scalar flavors
• Color-flavor reflection in the continuum limit of two-dimensional lattice gauge theories with scalar fields