Phase Diagram and Finite Temperature Properties of Negative Coupling Scalar Field Theory

TL;DR

This paper investigates the phase diagram and finite temperature behavior of a scalar field theory with negative quartic coupling, revealing its potential as a UV-complete, interacting model possibly relevant for the Higgs boson.

Contribution

It introduces a detailed analysis of negative coupling scalar field theory across dimensions and temperature, proposing it as a promising candidate for an interacting, UV-complete quantum field theory.

Findings

Negative coupling theory exhibits stable quantum behavior despite classical instability.

The phase diagram is mapped in dimensions one to four.

Potential implications for a UV-complete Higgs model.

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.