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A loophole in the proofs of quantum triviality and asymptotic freedom

Paul Romatschke, University of Colorado Boulder
Tuesday, October 10, 2023 - 3:00pm
PAT C-421

Back in 1973, Sidney Coleman and David Gross proved that only non-abelian gauge theories can have asymptotic freedom. More recently, Michael Aizenman and Hugo Duminil-Copin proved that scalar field theories are quantum trivial in four dimensions. Both of these important proofs have the same loophole: they assume that the coupling constant in the UV is positive definite. While a reasonable classical physics assumption, the results obtained in non-Hermitian (PT-symmetric) quantum mechanics indicate that certain field theories with negative coupling exist and fulfill the basic requirements of unitarity and stability. I will show an explicit calculation on how a particular field theory (the O(N) model) in 3+1 dimensions exploits this loophole, leading to a candidate for an asymptotically free interacting scalar field theory, and a potential alternative to the Standard Model Higgs sector with one less parameter.

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