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Phase diagram and finite temperature properties of negative coupling scalar field theory

Paul Romatschke

  • Institut für Theoretische Physik, TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria

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Phys. Rev. D 114, 056011 – Published 9 September, 2026

DOI: https://doi.org/10.1103/8p6t-nnsj

Abstract

In this work, I consider scalar field theory with negative quartic self-interaction, corresponding to an upside-down classical potential. Despite not possessing a classically stable ground state, such potentials are known to behave properly when treated quantum mechanically, leading to stable and unitary time evolution. Using two different saddle-point expansions for the same theory, I discuss the phase diagram in terms of bare parameters in Euclidean dimensions one to four, as well as the generalization to finite temperature. Comparing to other methods where available, I find that negative coupling field theory is a promising candidate for an interacting scalar field theory in the continuum. In particular, in four dimensions it exploits a loophole in mathematical proofs of quantum triviality, suggesting that negative coupling scalar field theory could offer a UV-complete and interacting description of the Higgs.

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Phys. Rev. D 114, 056011– Published 9 September, 2026
  • Received 29 June 2026
  • Accepted 5 August 2026
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