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)×Z2 symmetry at zero temperature. Using conformal perturbation theory we establish Z2 symmetry is broken at finite temperature for N>17. Similar to recent constructions of [N. Chai et al., Phys. Rev. D 102, 065014 (2020)., N. Chai et al., Phys. Rev. Lett. 125, 131603 (2020).], 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. [ABSTRACT FROM AUTHOR]