A model of persistent breaking of discrete symmetry

Understand

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 $O(N)\times \mathbb{Z}_2$ symmetry at zero temperature.
• Using conformal perturbation theory we establish $\mathbb{Z}_2$ symmetry is broken at finite temperature for $N>10$.
• Similar to recent constructions, in the infinite $N$ limit our model has a non-trivial conformal manifold, a moduli space of vacua, which gets deformed at finite temperature.