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Nonperturbative infrared finiteness in super-renormalisable scalar quantum field theory

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

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 SU(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, Phys. Rev. D 23, 2291 (1981)PRVDAQ0556-282110.1103/PhysRevD.23.2291, T. Appelquist, Phys. Rev. D 23, 2305 (1981)PRVDAQ0556-282110.1103/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.

cond-mat.stat-mech, hep-lat, hep-th
1079-7114
Cossu, Guido
d09be903-90c4-40c9-9fe1-f416f5dc15ce
Del Debbio, Luigi
4820afb6-c91b-4b30-a197-4805ebbc3c01
Juttner, Andreas
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
Kitching-Morley, Ben
2fae2631-6c01-4522-800f-44308ea5ecf1
Lee, Joseph K. L.
d7033d35-436a-44d8-a1db-5c07ad9cb6e9
Portelli, Antonin
3f93d454-9e78-44b0-9640-ee5ffedf05e3
Rocha, Henrique Bergallo
4cc4bd22-ef05-430a-b91d-f28ece2d9b1b
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Cossu, Guido
d09be903-90c4-40c9-9fe1-f416f5dc15ce
Del Debbio, Luigi
4820afb6-c91b-4b30-a197-4805ebbc3c01
Juttner, Andreas
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
Kitching-Morley, Ben
2fae2631-6c01-4522-800f-44308ea5ecf1
Lee, Joseph K. L.
d7033d35-436a-44d8-a1db-5c07ad9cb6e9
Portelli, Antonin
3f93d454-9e78-44b0-9640-ee5ffedf05e3
Rocha, Henrique Bergallo
4cc4bd22-ef05-430a-b91d-f28ece2d9b1b
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09

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]. (doi:10.1103/PhysRevLett.126.221601).

Record type: Article

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 SU(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, Phys. Rev. D 23, 2291 (1981)PRVDAQ0556-282110.1103/PhysRevD.23.2291, T. Appelquist, Phys. Rev. D 23, 2305 (1981)PRVDAQ0556-282110.1103/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.

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2009.14768v1 - Author's Original
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LZ16649-9 - Accepted Manuscript
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Submitted date: 30 September 2020
Accepted/In Press date: 29 April 2021
Published date: 4 June 2021
Additional Information: Funding Information: The authors would like to warmly thank Pavlos Vranas for his valuable support during the early stages of this project. We would like to thank Masanori Hanada for collaboration at early stages for this project. A. J. and K. S. acknowledge funding from STFC consolidated grants ST/P000711/1 and ST/T000775/1. A. P. is supported in part by UK STFC grant ST/P000630/1. A. P., J. K. L. L., and H. B. R are funded in part by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme under Grant Agreement No. 757646 and A. P. additionally Grant Agreement No. 813942. J. K. L. L. is also partly funded by the Croucher Foundation through the Croucher Scholarships for Doctoral Study. B. K. M. was supported by the EPSRC Centre for Doctoral Training in Next Generation Computational Modelling Grant No. EP/L015382/1. L. D. D. is supported by an STFC Consolidated Grant, ST/P0000630/1, and a Royal Society Wolfson Research Merit Award, WM140078. Simulations produced for this work were performed using the Grid Library (), which is free software under gpl v2. This work was performed using the Cambridge Service for Data Driven Discovery (CSD3), part of which is operated by the University of Cambridge Research Computing on behalf of the STFC DiRAC HPC Facility (). The DiRAC component of CSD3 was funded by BEIS capital funding via STFC capital grants ST/P002307/1 and ST/R002452/1 and STFC operations grant ST/R00689X/1. DiRAC is part of the National e-Infrastructure. The authors acknowledge the use of the IRIDIS High-Performance Computing Facility and associated support services at the University of Southampton in the completion of this work. Publisher Copyright: © 2021 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.
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 iD orcid.org/0000-0002-3978-0927
ORCID for Ben Kitching-Morley: ORCID iD orcid.org/0000-0003-3150-401X
ORCID for Kostas Skenderis: ORCID iD orcid.org/0000-0003-4509-5472

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Date deposited: 10 May 2021 16:30
Last modified: 17 Mar 2024 03:27

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Contributors

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

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