A model of persistent breaking of discrete symmetry

Abstract

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. 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.

corrections and references added

References in corpus (15)

• Asymptotic safety guaranteed
• On the Hohenberg-Mermin-Wagner theorem and its limitations
• Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains
• Thermal Order in Conformal Theories
• QCD on a small circle
• Higher Anomalies, Higher Symmetries, and Cobordisms III: QCD Matter Phases Anew
• Thermal order in holographic CFTs and no-hair theorem violation in black branes
• Critical behavior of the Ising model with long range interactions
• The free and safe fate of symmetry non-restoration
• The fate of the conformal order
• Thermal order in large N conformal gauge theories
• The bi-conical vector model at $1/N$
• SUGRA/Strings like to be bald
• Symmetry breaking at high temperatures in large N gauge theories
• Compactified holographic conformal order

Cited by in corpus (8)

• A model of persistent breaking of continuous symmetry
• Compactified holographic conformal order
• Polyakov's confinement mechanism for generalized Maxwell theory
• Long-range fermions and critical dualities
• Spontaneous breaking of finite group symmetries at all temperatures
• Quantum phase transitions in a bidimensional $O(N)\times {\mathbb{Z}}_2$ scalar field model
• Critical long-range vector model in the UV
• Long-Range Vector Models at Large N