A structural test for the conformal invariance of the critical 3d Ising model

How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current — a non-conserved vector operator of dimension exactly (d − 1), whose divergence expresses the trace of the stress tensor. We...

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Detalles Bibliográficos
Autores principales: Meneses, Simão, Penedones, João, Rychkov, Slava, Viana Parente Lopes, J.M., Yvernay, Pierre
Lenguaje:eng
Publicado: 2018
Materias:
hep-lat
Particle Physics - Lattice
cond-mat.stat-mech
hep-th
Particle Physics - Theory
Acceso en línea:https://dx.doi.org/10.1007/JHEP04(2019)115
http://cds.cern.ch/record/2305770
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author Meneses, Simão
Penedones, João
Rychkov, Slava
Viana Parente Lopes, J.M.
Yvernay, Pierre
author_facet Meneses, Simão
Penedones, João
Rychkov, Slava
Viana Parente Lopes, J.M.
Yvernay, Pierre
author_sort Meneses, Simão
collection CERN
description How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current — a non-conserved vector operator of dimension exactly (d − 1), whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via lattice Monte Carlo simulations, using the critical 3d Ising model as an example. Our results put a lower bound Δ$_{V}$ > 5.0 on the scaling dimension of the lowest virial current candidate V, well above 2 expected for the true virial current. This implies that the critical 3d Ising model has no virial current, providing a structural explanation for the conformal invariance of the model.
id cern-2305770
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2018
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spelling cern-23057702023-10-04T08:54:00Zdoi:10.1007/JHEP04(2019)115http://cds.cern.ch/record/2305770engMeneses, SimãoPenedones, JoãoRychkov, SlavaViana Parente Lopes, J.M.Yvernay, PierreA structural test for the conformal invariance of the critical 3d Ising modelhep-latParticle Physics - Latticecond-mat.stat-mechhep-thParticle Physics - TheoryHow can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current — a non-conserved vector operator of dimension exactly (d − 1), whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via lattice Monte Carlo simulations, using the critical 3d Ising model as an example. Our results put a lower bound Δ$_{V}$ > 5.0 on the scaling dimension of the lowest virial current candidate V, well above 2 expected for the true virial current. This implies that the critical 3d Ising model has no virial current, providing a structural explanation for the conformal invariance of the model.How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current -- a non-conserved vector operator of dimension exactly $(d-1)$, whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via lattice Monte Carlo simulations, using the critical 3d Ising model as an example. Our results put a lower bound $\Delta_V>5.0$ on the scaling dimension of the lowest virial current candidate $V$, well above 2 expected for the true virial current. This implies that the critical 3d Ising model has no virial current, providing a structural explanation for the conformal invariance of the model.arXiv:1802.02319oai:cds.cern.ch:23057702018-02-07
spellingShingle hep-lat
Particle Physics - Lattice
cond-mat.stat-mech
hep-th
Particle Physics - Theory
Meneses, Simão
Penedones, João
Rychkov, Slava
Viana Parente Lopes, J.M.
Yvernay, Pierre
A structural test for the conformal invariance of the critical 3d Ising model
title A structural test for the conformal invariance of the critical 3d Ising model
title_full A structural test for the conformal invariance of the critical 3d Ising model
title_fullStr A structural test for the conformal invariance of the critical 3d Ising model
title_full_unstemmed A structural test for the conformal invariance of the critical 3d Ising model
title_short A structural test for the conformal invariance of the critical 3d Ising model
title_sort structural test for the conformal invariance of the critical 3d ising model
topic hep-lat
Particle Physics - Lattice
cond-mat.stat-mech
hep-th
Particle Physics - Theory
url https://dx.doi.org/10.1007/JHEP04(2019)115
http://cds.cern.ch/record/2305770
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