Renormalization of the energy-momentum tensor in three-dimensional scalar SU(N) theories using the Wilson flow
Renormalization of the energy-momentum tensor in three-dimensional scalar SU(N) theories using the Wilson flow
 
  A nonperturbative determination of the energy-momentum tensor is essential for understanding the physics of strongly coupled systems. The ability of the Wilson flow to eliminate divergent contact terms makes it a practical method for renormalizing the energy-momentum tensor on the lattice. In this paper, we utilize the Wilson flow to define a procedure to renormalize the energy-momentum tensor for a three-dimensional massless scalar field in the adjoint of SU(N) with a φ4 interaction on the lattice. In this theory the energy-momentum tensor can mix with φ2 and we present numerical results for the mixing coefficient for the N=2 theory.
hep-lat, hep-th
  
  
  
    
      Debbio, Luigi Del
      
        4820afb6-c91b-4b30-a197-4805ebbc3c01
      
     
  
    
      Dobson, Elizabeth
      
        a511f10f-c17e-4416-9ff5-4da1a2a4b017
      
     
  
    
      Jüttner, Andreas
      
        a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
      
     
  
    
      Kitching-Morley, Ben
      
        2fae2631-6c01-4522-800f-44308ea5ecf1
      
     
  
    
      Lee, Joseph K. L.
      
        d7033d35-436a-44d8-a1db-5c07ad9cb6e9
      
     
  
    
      Nourry, Valentin
      
        a860a8dd-d375-4b42-ae00-7a9d0d50c574
      
     
  
    
      Portelli, Antonin
      
        3a105e9a-38d9-4ae0-b0f1-95623a5ad81f
      
     
  
    
      Rocha, Henrique Bergallo
      
        4cc4bd22-ef05-430a-b91d-f28ece2d9b1b
      
     
  
    
      Skenderis, Kostas
      
        09f32871-ffb1-4f4a-83bc-df05f4d17a09
      
     
  
  
   
  
  
    
    
  
    
    
  
    
      3 June 2021
    
    
  
  
    
      Debbio, Luigi Del
      
        4820afb6-c91b-4b30-a197-4805ebbc3c01
      
     
  
    
      Dobson, Elizabeth
      
        a511f10f-c17e-4416-9ff5-4da1a2a4b017
      
     
  
    
      Jüttner, Andreas
      
        a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
      
     
  
    
      Kitching-Morley, Ben
      
        2fae2631-6c01-4522-800f-44308ea5ecf1
      
     
  
    
      Lee, Joseph K. L.
      
        d7033d35-436a-44d8-a1db-5c07ad9cb6e9
      
     
  
    
      Nourry, Valentin
      
        a860a8dd-d375-4b42-ae00-7a9d0d50c574
      
     
  
    
      Portelli, Antonin
      
        3a105e9a-38d9-4ae0-b0f1-95623a5ad81f
      
     
  
    
      Rocha, Henrique Bergallo
      
        4cc4bd22-ef05-430a-b91d-f28ece2d9b1b
      
     
  
    
      Skenderis, Kostas
      
        09f32871-ffb1-4f4a-83bc-df05f4d17a09
      
     
  
       
    
 
  
    
      
  
  
  
  
  
  
    Debbio, Luigi Del, Dobson, Elizabeth, Jüttner, Andreas, Kitching-Morley, Ben, Lee, Joseph K. L., Nourry, Valentin, Portelli, Antonin, Rocha, Henrique Bergallo and Skenderis, Kostas
  
  
  
  
   
    (2021)
  
  
    
    Renormalization of the energy-momentum tensor in three-dimensional scalar SU(N) theories using the Wilson flow.
  
  
  
  
    Physical Review D, 103 (11), [114501].
  
   (doi:10.1103/PhysRevD.103.114501). 
  
  
   
  
  
  
  
  
   
  
    
    
      
        
          Abstract
          A nonperturbative determination of the energy-momentum tensor is essential for understanding the physics of strongly coupled systems. The ability of the Wilson flow to eliminate divergent contact terms makes it a practical method for renormalizing the energy-momentum tensor on the lattice. In this paper, we utilize the Wilson flow to define a procedure to renormalize the energy-momentum tensor for a three-dimensional massless scalar field in the adjoint of SU(N) with a φ4 interaction on the lattice. In this theory the energy-momentum tensor can mix with φ2 and we present numerical results for the mixing coefficient for the N=2 theory.
         
      
      
        
          
            
  
    Text
 DZ12469
     - Accepted Manuscript
   
  
  
    
  
 
          
            
          
            
           
            
           
        
          
        
        
       
    
   
  
  
  More information
  
    
      Submitted date: 30 September 2020
 
    
      Accepted/In Press date: 16 April 2021
 
    
      Published date: 3 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 thank Masanori Hanada for collaboration at initial stages of this project. Simulations produced for this work were performed using the Grid and Hadrons libraries, which are free software under GPLv2. The data analysis was based on the LatAnalyze library , which is free software under GPLv3. 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. 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., V. N., and H. B. R. are funded in part by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program under Grant Agreement No. 757646 and A. P. additionally under 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. V. N. is partially funded by the research internship funds of the Université Paris-Saclay. L. D. D. is supported by an STFC Consolidated Grant, ST/P0000630/1, and a Royal Society Wolfson Research Merit Award, WM140078.
Publisher Copyright:
© 2021 authors. Published by the American Physical Society.
      
    
  
    
  
    
  
    
     
    
  
    
     
        Keywords:
        hep-lat, hep-th
      
    
  
    
  
    
  
  
  
    
  
    
  
    
  
  
        Identifiers
        Local EPrints ID: 448897
        URI: http://eprints.soton.ac.uk/id/eprint/448897
        
          
        
        
        
          ISSN: 2470-0029
        
        
          PURE UUID: b61fec91-a477-45c6-b553-afdb2898af76
        
  
    
        
          
        
    
        
          
        
    
        
          
            
              
            
          
        
    
        
          
            
              
            
          
        
    
        
          
        
    
        
          
        
    
        
          
        
    
        
          
        
    
        
          
            
              
            
          
        
    
  
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  Date deposited: 10 May 2021 16:31
  Last modified: 17 Mar 2024 03:27
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      Contributors
      
          
          Author:
          
            
            
              Luigi Del Debbio
            
          
        
      
          
          Author:
          
            
            
              Elizabeth Dobson
            
          
        
      
        
      
          
          Author:
          
            
              
              
                Ben Kitching-Morley
              
              
                 
              
            
            
          
         
      
          
          Author:
          
            
            
              Joseph K. L. Lee
            
          
        
      
          
          Author:
          
            
            
              Valentin Nourry
            
          
        
      
          
          Author:
          
            
            
              Antonin Portelli
            
          
        
      
          
          Author:
          
            
            
              Henrique Bergallo Rocha
            
          
        
      
        
      
      
      
    
  
   
  
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