# A model of persistent breaking of continuous symmetry

### Submission summary

 As Contributors: Noam Chai Arxiv Link: https://arxiv.org/abs/2111.02474v2 (pdf) Date accepted: 2022-05-23 Date submitted: 2022-04-14 02:43 Submitted by: Chai, Noam Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### 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 $N$.

Published as SciPost Phys. 12, 181 (2022)

### Submission & Refereeing History

#### Published as SciPost Phys. 12, 181 (2022)

Resubmission 2111.02474v2 on 14 April 2022
Submission scipost_202112_00049v1 on 21 December 2021

## Reports on this Submission

### Report

The authors' editing satisfied almost all my requests. (Just to be clear, with "missing articles" I means missing "the" and "a, an"). I recommend the paper for publication on SciPost in its current form.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Report

The authors' changes after my initial referee report are sufficient. I recommend publication to SciPost Physics.

• validity: top
• significance: good
• originality: high
• clarity: top
• formatting: excellent
• grammar: excellent