Nonperturbative Infrared Finiteness in a Superrenormalizable Scalar Quantum Field Theory
Abstract
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 φ4 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), 10.1103/PhysRevD.23.2291, T. Appelquist et al., Phys. Rev. D 23, 2305 (1981), 10.1103/PhysRevD.23.2305] 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.
- Publication:
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Physical Review Letters
- Pub Date:
- June 2021
- DOI:
- 10.1103/PhysRevLett.126.221601
- arXiv:
- arXiv:2009.14768
- Bibcode:
- 2021PhRvL.126v1601C
- Keywords:
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- High Energy Physics - Lattice;
- Condensed Matter - Statistical Mechanics;
- High Energy Physics - Theory
- E-Print:
- Version accepted for publication in PRL, added references, updated plots, extended discussion of IR behaviour in perturbation theory and EFT