Model of Persistent Breaking of Discrete Symmetry

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.