Abstract
We show there exist UV-complete field-theoretic models in general dimension, including 2+1, with the spontaneous breaking of a global symmetry, which persists to the arbitrarily high temperatures. Our example is a conformal vector model with the O(N)×Z_{2} symmetry at zero temperature. Using conformal perturbation theory we establish Z_{2} symmetry is broken at finite temperature for N>17. Similar to recent constructions of [N. Chai et al., Phys. Rev. D 102, 065014 (2020).PRVDAQ2470-001010.1103/PhysRevD.102.065014, 2N. Chai et al., Phys. Rev. Lett. 125, 131603 (2020).PRLTAO0031-900710.1103/PhysRevLett.125.131603], in the infinite N limit our model has a nontrivial conformal manifold, a moduli space of vacua, which gets deformed at finite temperature. Furthermore, in this regime the model admits a persistent breaking of O(N) in 2+1 dimensions, therefore providing another example where the Coleman-Hohenberg-Mermin-Wagner theorem can be bypassed.
Highlights
Introduction.—The phenomenon of spontaneous symmetry breaking is ubiquitous: many real systems as well as field theoretic models exhibit spontaneous breaking of both discrete and continuous symmetries at zero or sufficiently small temperature
We show there exist UV-complete field-theoretic models in general dimension, including 2 þ 1, with the spontaneous breaking of a global symmetry, which persists to the arbitrarily high temperatures
In this regime the model admits a persistent breaking of OðNÞ in 2 þ 1 dimensions, providing another example where the ColemanHohenberg-Mermin-Wagner theorem can be bypassed
Summary
We show there exist UV-complete field-theoretic models in general dimension, including 2 þ 1, with the spontaneous breaking of a global symmetry, which persists to the arbitrarily high temperatures. In this Letter we answer this question by constructing UV-complete field-theoretical models in diverse dimensions which exhibit persistent breaking of both discrete and continuous symmetries For lattice systems it is well appreciated the symmetry is restored for temperates large in comparison with the lattice spacing [1]. This suggests nonlocal field theories, which may result from such lattice models in the continuous limit may be immune to various no-go results To better illustrate this idea we briefly mention Coleman’s no-go theorem [7], which in d 1⁄4 1 þ 1 excludes spontaneous symmetry breaking because the corresponding Goldstone bosons, being massless, would have infrared divergences.
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