Phase Diagram and Finite Temperature Properties of Negative Coupling Scalar Field Theory
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908902724993024 |
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| author | Romatschke, Paul |
| author_facet | Romatschke, Paul |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_19877 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Phase Diagram and Finite Temperature Properties of Negative Coupling Scalar Field Theory Romatschke, Paul High Energy Physics - Theory Mathematical Physics Nuclear Theory 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. |
| title | Phase Diagram and Finite Temperature Properties of Negative Coupling Scalar Field Theory |
| topic | High Energy Physics - Theory Mathematical Physics Nuclear Theory |
| url | https://arxiv.org/abs/2603.19877 |