Nonperturbative Infrared Finiteness in a Superrenormalizable Scalar Quantum Field Theory

Guido Cossu, Luigi Del Debbio, Andreas Jüttner, Ben Kitching-Morley, Joseph K. L. Lee, Antonin Portelli, Henrique Bergallo Rocha, Kostas Skenderis

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We present a study of the IR behavior of a three-dimensional superrenormalizable quantum field theory consisting of a scalar field in the adjoint of S U (N) with a φ 4 interaction. A bare mass is required for the theory to be massless at the quantum level. In perturbation theory, the critical mass is ambiguous due to IR divergences, and we indeed find that at two loops in lattice perturbation theory the critical mass diverges logarithmically. It was conjectured long ago in [R. Jackiw et al., Phys. Rev. D 23, 2291 (1981), T. Appelquist et al., Phys. Rev. D 23, 2305 (1981)] that superrenormalizable theories are nonperturbatively IR finite, with the coupling constant playing the role of an IR regulator. Using a combination of Markov Chain Monte Carlo simulations of the lattice-regularized theory, frequentist and Bayesian data analysis, and considerations of a corresponding effective theory, we gather evidence that this is indeed the case.
Original languageEnglish
Article number221601
Pages (from-to)1-7
JournalPhysical Review Letters
Issue number22
Publication statusPublished - 4 Jun 2021


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