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Deformations of infrared-conformal theories in two dimensions
We study two exactly solvable two-dimensional conformal models, the critical Ising model and the Sommerfield model, on the lattice. We show that finite-size effects are important and depend on the aspect ratio of the lattice. In particular, we demonstrate how to obtain the correct massless behavior...
Autores principales: | , |
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Lenguaje: | eng |
Publicado: |
2014
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Materias: | |
Acceso en línea: | https://dx.doi.org/10.22323/1.214.0243 http://cds.cern.ch/record/1953098 |
_version_ | 1780944348625502208 |
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author | Akerlund, Oscar de Forcrand, Philippe |
author_facet | Akerlund, Oscar de Forcrand, Philippe |
author_sort | Akerlund, Oscar |
collection | CERN |
description | We study two exactly solvable two-dimensional conformal models, the critical Ising model and the Sommerfield model, on the lattice. We show that finite-size effects are important and depend on the aspect ratio of the lattice. In particular, we demonstrate how to obtain the correct massless behavior from an infinite tower of finite-size-induced masses and show that it is necessary to first take the cylindrical geometry limit in order to get correct results. In the Sommerfield model we also introduce a mass deformation to measure the mass anomalous dimension, $\gamma_m$. We find that the explicit scale breaking of the lattice setup induces corrections which must be taken into account in order to reproduce $\gamma_m$ at the infrared fixed point. These results can be used to improve the methodology in the search for the conformal window in QCD-like theories with many flavors. |
id | cern-1953098 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2014 |
record_format | invenio |
spelling | cern-19530982022-08-10T21:10:11Zdoi:10.22323/1.214.0243http://cds.cern.ch/record/1953098engAkerlund, Oscarde Forcrand, PhilippeDeformations of infrared-conformal theories in two dimensionsParticle Physics - LatticeWe study two exactly solvable two-dimensional conformal models, the critical Ising model and the Sommerfield model, on the lattice. We show that finite-size effects are important and depend on the aspect ratio of the lattice. In particular, we demonstrate how to obtain the correct massless behavior from an infinite tower of finite-size-induced masses and show that it is necessary to first take the cylindrical geometry limit in order to get correct results. In the Sommerfield model we also introduce a mass deformation to measure the mass anomalous dimension, $\gamma_m$. We find that the explicit scale breaking of the lattice setup induces corrections which must be taken into account in order to reproduce $\gamma_m$ at the infrared fixed point. These results can be used to improve the methodology in the search for the conformal window in QCD-like theories with many flavors.arXiv:1410.1178CERN-PH-TH-2014-185oai:cds.cern.ch:19530982014-10-05 |
spellingShingle | Particle Physics - Lattice Akerlund, Oscar de Forcrand, Philippe Deformations of infrared-conformal theories in two dimensions |
title | Deformations of infrared-conformal theories in two dimensions |
title_full | Deformations of infrared-conformal theories in two dimensions |
title_fullStr | Deformations of infrared-conformal theories in two dimensions |
title_full_unstemmed | Deformations of infrared-conformal theories in two dimensions |
title_short | Deformations of infrared-conformal theories in two dimensions |
title_sort | deformations of infrared-conformal theories in two dimensions |
topic | Particle Physics - Lattice |
url | https://dx.doi.org/10.22323/1.214.0243 http://cds.cern.ch/record/1953098 |
work_keys_str_mv | AT akerlundoscar deformationsofinfraredconformaltheoriesintwodimensions AT deforcrandphilippe deformationsofinfraredconformaltheoriesintwodimensions |