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  • Open Access

Spontaneous spacetime parity breaking without thermal restoration

Bilal Hawashin1,*, Michael M. Scherer1,†, Michael Smolkin2,‡, and Lev Yung2,§

  • *Contact author: hawashin@tp3.rub.de
  • †Contact author: scherer@tp3.rub.de
  • ‡Contact author: michael.smolkin@mail.huji.ac.il
  • §Contact author: lev.yung@mail.huji.ac.il
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Phys. Rev. D 114, 065005 – Published 8 September, 2026

DOI: https://doi.org/10.1103/cc6w-syd1

Abstract

We provide strong evidence for spontaneous breaking of spacetime parity persisting to arbitrarily high temperatures in a local, unitary, ultraviolet-complete quantum field theory in 2+1 dimensions. The theory is defined by a renormalization group trajectory, triggered by a relevant deformation of a conformal field theory, consisting of a critical biconical vector model and a free massless Dirac fermion. This deformation couples the fermion to the scalar sector, generating a renormalization group flow that terminates at a nontrivial infrared fixed point described by a conformal Gross-Neveu-Yukawa model and a decoupled critical vector model. By construction, the quantum field theory is parity invariant at zero temperature. However, we show that at sufficiently high temperatures, parity symmetry is spontaneously broken and remains so even in the infinite-temperature limit. Our analysis relies on both, perturbative renormalization group techniques in 4−ε dimensions and functional renormalization group techniques directly in 2+1 dimensions.

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Phys. Rev. D 114, 065005– Published 8 September, 2026
  • Received 28 August 2025
  • Accepted 3 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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