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
  
  
  
    
      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
      
     
  
  
   
  
  
    
    
  
    
    
  
    
      4 June 2021
    
    
  
  
    
      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). 
  
  
   
  
  
  
  
  
   
  
    
    
      
        
          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
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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
        
  
    
        
          
        
    
        
          
        
    
        
          
            
              
            
          
        
    
        
          
            
              
            
          
        
    
        
          
        
    
        
          
        
    
        
          
        
    
        
          
            
              
            
          
        
    
  
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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:
          
            
              
              
                Ben Kitching-Morley
              
              
                 
              
            
            
          
         
      
          
          Author:
          
            
            
              Joseph K. L. Lee
            
          
        
      
          
          Author:
          
            
            
              Antonin Portelli
            
          
        
      
          
          Author:
          
            
            
              Henrique Bergallo Rocha
            
          
        
      
        
      
      
      
    
  
   
  
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