A model of persistent breaking of continuous symmetry

Chai, Noam; Dymarsky, Anatoly; Goykhman, Mikhail; Sinha, Ritam; Smolkin, Michael

doi:10.21468/SciPostPhys.12.6.181

SciPost Physics

A model of persistent breaking of continuous symmetry

Noam Chai, Anatoly Dymarsky, Mikhail Goykhman, Ritam Sinha, Michael Smolkin

SciPost Phys. 12, 181 (2022) · published 1 June 2022

doi: 10.21468/SciPostPhys.12.6.181
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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 $N$.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.12.6.181
TI  - A model of persistent breaking of continuous symmetry
PY  - 2022/06/01
UR  - https://www.scipost.org/SciPostPhys.12.6.181
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 12
IS  - 6
SP  - 181
A1  - Chai, Noam
AU  - Dymarsky, Anatoly
AU  - Goykhman, Mikhail
AU  - Sinha, Ritam
AU  - Smolkin, Michael
AB  - 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 $N$.
ER  -

@Article{10.21468/SciPostPhys.12.6.181,
	title={{A model of persistent breaking of continuous symmetry}},
	author={Noam Chai and Anatoly Dymarsky and Mikhail Goykhman and Ritam Sinha and Michael Smolkin},
	journal={SciPost Phys.},
	volume={12},
	pages={181},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.12.6.181},
	url={https://scipost.org/10.21468/SciPostPhys.12.6.181},
}

Cited by 7

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¹ Noam Chai,
² ³ Anatoly Dymarsky,
¹ ⁴ Mikhail Goykhman,
¹ Ritam Sinha,
¹ Michael Smolkin

Funders for the research work leading to this publication