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# Nonperturbative infrared finiteness in super-renormalisable scalar quantum field theory

Cossu, Guido, Del Debbio, Luigi, Juttner, Andreas, Kitching-Morley, Ben, Lee, Joseph K. L., Portelli, Antonin, Rocha, Henrique Bergallo and Skenderis, Kostas (2021) Nonperturbative infrared finiteness in super-renormalisable scalar quantum field theory. Physical Review Letters, 126 (22), [221601].

Record type: Article

## Abstract

We present a study of the IR behaviour of a three-dimensional super-renormalisable quantum field theory (QFT) consisting of a scalar field in the adjoint of $SU(N)$ with a $\varphi^4$ 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 infrared (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 [Jackiw 1980, Appelquist 1981] that super-renormalisable 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-regularised theory, both frequentist and Bayesian data analysis, and considerations of a corresponding effective theory we gather evidence that this is indeed the case.

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2009.14768v1 - Author's Original
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LZ16649-9 - Accepted Manuscript
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## More information

Submitted date: 30 September 2020
Accepted/In Press date: 29 April 2021
Published date: 4 June 2021
Additional Information: 6 pages plus supplementary material (7 pages)
Keywords: cond-mat.stat-mech, hep-lat, hep-th

## Identifiers

Local EPrints ID: 448895
URI: http://eprints.soton.ac.uk/id/eprint/448895
ISSN: 1079-7114
PURE UUID: 6ed34c7f-68ca-471d-8ad9-f3a4683a0b6f
ORCID for Andreas Juttner: orcid.org/0000-0002-3978-0927
ORCID for Kostas Skenderis: orcid.org/0000-0003-4509-5472

## Catalogue record

Date deposited: 10 May 2021 16:30
Last modified: 28 Apr 2022 02:06

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## Contributors

Author: Guido Cossu
Author: Luigi Del Debbio
Author: Andreas Juttner
Author: Ben Kitching-Morley
Author: Joseph K. L. Lee
Author: Antonin Portelli
Author: Henrique Bergallo Rocha

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