A structural test for the conformal invariance of the critical 3d Ising model
Abstract 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 te...
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2019-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP04(2019)115 |
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doaj-3867a84da1f149f9b934c3be750f74bf2020-11-25T02:55:08ZengSpringerOpenJournal of High Energy Physics1029-84792019-04-012019412710.1007/JHEP04(2019)115A structural test for the conformal invariance of the critical 3d Ising modelSimão Meneses0João Penedones1Slava Rychkov2J. M. Viana Parente Lopes3Pierre Yvernay4Centro de Física das Universidades do Minho e Porto, Departamento de Engenharia Física, Faculdade de Engenharia and Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do PortoInstitute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)Institut des Hautes Études ScientifiquesCentro de Física das Universidades do Minho e Porto, Departamento de Engenharia Física, Faculdade de Engenharia and Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do PortoTheoretical Physics Department, CERNAbstract 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.http://link.springer.com/article/10.1007/JHEP04(2019)115Conformal and W SymmetryConformal Field TheoryLattice Quantum Field TheoryRenormalization Group |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Simão Meneses João Penedones Slava Rychkov J. M. Viana Parente Lopes Pierre Yvernay |
| spellingShingle |
Simão Meneses João Penedones Slava Rychkov J. M. Viana Parente Lopes Pierre Yvernay A structural test for the conformal invariance of the critical 3d Ising model Journal of High Energy Physics Conformal and W Symmetry Conformal Field Theory Lattice Quantum Field Theory Renormalization Group |
| author_facet |
Simão Meneses João Penedones Slava Rychkov J. M. Viana Parente Lopes Pierre Yvernay |
| author_sort |
Simão Meneses |
| title |
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_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_sort |
structural test for the conformal invariance of the critical 3d ising model |
| publisher |
SpringerOpen |
| series |
Journal of High Energy Physics |
| issn |
1029-8479 |
| publishDate |
2019-04-01 |
| description |
Abstract 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. |
| topic |
Conformal and W Symmetry Conformal Field Theory Lattice Quantum Field Theory Renormalization Group |
| url |
http://link.springer.com/article/10.1007/JHEP04(2019)115 |
| work_keys_str_mv |
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