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Revisiting the ϕ6 theory in three dimensions at large N

Sandra Kvedaraitė1,*, Tom Steudtner2,†, and Max Uetrecht2,‡

  • *Contact author: skvedaraite@ugr.es
  • †Contact author: tom2.steudtner@tu-dortmund.de
  • ‡Contact author: max.uetrecht@tu-dortmund.de
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Phys. Rev. D 112, 056004 – Published 3 September, 2025

DOI: https://doi.org/10.1103/tnh4-7lnv

Abstract

We investigate the O(N)-symmetric ϕ6 theory in three spacetime dimensions using dimensional regularization and minimal subtraction. The predictions of other methods are scrutinized in a large-N expansion. We show how the tricritical line of fixed point emerges in a strict N→∞ limit but argue that it is not a physical manifestation. For the first time in this explicit manner, we compute the effective potential at next-to-leading order in the 1/N-expansion and discuss its stability. The Bardeen-Moshe-Bander phenomenon is also analysed at next-to-leading order, and we demonstrate that it disappears without breaking the scale invariance spontaneously. Our findings indicate that the UV fixed point found by Pisarski persists at large N.

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Phys. Rev. D 112, 056004– Published 3 September, 2025
  • Received 21 February 2025
  • Accepted 21 August 2025
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