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

Abstract

We address the interplay between global and local gauge non-Abelian symmetries in lattice gauge theories with multicomponent scalar fields. We consider two-dimensional lattice scalar non-Abelian gauge theories with a local SOðN c Þ (N c ≥ 3) and a global OðN f Þ invariance, obtained by partially gauging a maximally OðN f N c Þ-symmetric multicomponent scalar model. Correspondingly, the scalar fields belong to the coset S N f N c −1 =SOðN c Þ, where S N is the N-dimensional sphere. In agreement with the Mermin-Wagner theorem, these lattice SOðN c Þ gauge models with N f ≥ 3 do not have finite-temperature transitions related to the breaking of the global non-Abelian OðN f Þ 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 OðNÞ σ 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 N f −1 model.

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

“…The results presented in ref. [14] are in full agreement with the analysis presented here. In the following, we will present results for N c = 3, v = 0 and for N c = 2, 3, v > 0.…”

“…We have therefore investigated the zero-temperature behavior, to understand whether a continuum limit exists and, if it does, to identify the corresponding 2D quantum field theory. This work extend previous results [12][13][14][15], discussing the role played by the gauge representations and by the quartic scalar potential. For this purpose, we have identified the low-energy configurations, that are relevant in the zero-temperature limit, and we have derived effective models that are expected to describe the large-scale behavior of the system.…”

“…Results for v = 0 and N c = 2 have been already discussed in refs. [14] (N f = 3, 4) and [15] (where N f = 2, so that a finite-temperature BKT transition was observed). Indeed, for N c = 2 the model can be rewritten as an SO(3) gauge theory with fields in the fundamental representation of the gauge group.…”

“…We follow the strategy already employed in refs. [12][13][14][15]. In the FSS limit L → ∞ at L/ξ fixed, the RG invariant quantities R ξ and U , defined in eqs.…”

“…In the case of models characterized by both global and gauge symmetries, the asymptotic critical behavior is expected to arise from the interplay between the two different symmetries. For the purpose of understanding which features are relevant and which continuum limits are effectively realized, several 2D lattice models presenting both global and gauge continuous symmetries have been investigated [12][13][14][15], such as the lattice Abelian-Higgs model characterized by a global SU(N f ) (N f ≥ 2) and a local U(1) symmetry, the lattice scalar quantum chromodynamics with a global SU(N f ) and a local SU(N c ) symmetry, and a lattice SO(N c ) gauge model with a global O(N f ) and a local SO(N c ) symmetry. These studies support the following general conjecture: the universal low-temperature critical behavior, and therefore the continuum limit, of 2D lattice gauge models with scalar fields is the same as that of 2D σ models defined on symmetric spaces [3,16], which have the same global symmetry.…”