A model of persistent breaking of continuous symmetry

TL;DR

This paper introduces a UV-complete field theory model demonstrating persistent spontaneous breaking of continuous symmetry at all temperatures, generalizing previous discrete symmetry results and revealing a continuous family of fixed points.

Contribution

It constructs a new class of models with continuous symmetry breaking persisting at finite temperature, extending prior work on discrete symmetries and analyzing their conformal fixed points.

Findings

Weakly-coupled IR fixed points for N≥6

Persistent symmetry breaking at all temperatures

Existence of a continuous family of fixed points

Abstract

We consider a UV-complete field-theoretic model in general dimensions, including $d=2+1$, that exhibits spontaneous breaking of continuous symmetry, persisting to arbitrarily large temperatures. Our model consists of two copies of the long-range vector models, with $O(m)$ and $O(N-m)$ global symmetry groups, perturbed by double-trace operators. Using conformal perturbation theory we find weakly-coupled IR fixed points for $N\geq 6$ that reveal a spontaneous breaking of global symmetry. Namely, at finite temperature the lower rank group is broken, with the pattern persisting at all temperatures due to scale-invariance. We provide evidence that the models in question are unitary and invariant under full conformal symmetry. Our work generalizes recent results, which considered the particular case of $m=1$ and reported persistent breaking of the discrete $\mathbb{Z}_2=O(1)$. Furthermore, we show that this model exhibits a continuous family of weakly interacting field theories at finite $N$.