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.
Highlights
Lattice gauge models provide effective theories in various physical contexts, ranging from fundamental interactions [1,2] to emerging phenomena in condensed matter physics [3,4]
We will show that renormalization-group-invariant quantities defined in terms of Qfg in the non-Abelian gauge theory have the same universal behavior as the corresponding RPNf−1 quantities defined in terms of the local gaugeinvariant operator
We perform MC simulations, using the same upgrading algorithm employed in Ref. [10] for threedimensional lattice SOðNcÞ gauge models
Summary
Lattice gauge models provide effective theories in various physical contexts, ranging from fundamental interactions [1,2] to emerging phenomena in condensed matter physics [3,4]. [6,7] provide numerical evidence that the asymptotic low-temperature behavior of these 2D lattice gauge models always belongs to the universality class of the 2D CPNf−1 field theory [5]. The local gauge symmetry apparently does not play any role: models with different gauge symmetry but with the same global invariance have the same large-scale low-temperature behavior These results may be interpreted as numerical evidence of a more general conjecture [7]: the renormalization-group flow determining the asymptotic low-temperature behavior is generally controlled by the 2D statistical field theories associated with the symmetric spaces [5,8] that have the same global symmetry. According to the Mermin-Wagner theorem [9], lattice SOðNcÞ gauge theories are not expected to show finite-temperature transitions with a low-temperature phase in which the global OðNfÞ symmetry is broken. We will show that renormalization-group-invariant quantities defined in terms of Qfg in the non-Abelian gauge theory have the same universal behavior as the corresponding RPNf−1 quantities defined in terms of the local gaugeinvariant operator
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