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  • Letter
  • Open Access

Goldstone bosons at nonzero temperature

Peter Lowdon and Owe Philipsen

  • ITP, Goethe-Universität Frankfurt am Main, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany

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Phys. Rev. D 112, L061701 – Published 2 September, 2025

DOI: https://doi.org/10.1103/jsvd-jcgy

Abstract

Spontaneous symmetry breaking in quantum field theories at nonzero temperature still holds fundamental open questions, in particular what happens to vacuum Goldstone bosons when the temperature is increased. By investigating a complex scalar field theory on the lattice we demonstrate that Goldstone bosons at nonzero temperature behave like screened massless particlelike excitations, so-called thermoparticles, which continue to exist even in the symmetry-restored phase of the theory. We provide nonperturbative evidence for the functional form of the Goldstone mode’s dissipative behavior, and determine its corresponding spectral properties. Since the persistence of thermal Goldstone modes within symmetry-restored phases is predicted to be a model-independent characteristic, this has fundamental consequences for systems in which continuous symmetries are restored at high temperatures.

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Phys. Rev. D 112, L061701– Published 2 September, 2025
  • Received 20 February 2025
  • Accepted 19 August 2025
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