Bootstrapping the minimal 3D SCFT
Abstract We study the conformal bootstrap constraints for 3D conformal field theories with a ℤ 2 or parity symmetry, assuming a single relevant scalar operator ϵ that is invariant under the symmetry. When there is additionally a single relevant odd scalar σ, we map out the allowed space of dimension...
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Online Access: | http://link.springer.com/article/10.1007/JHEP11(2018)140 |
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doaj-62346854d449470ba3d4b416c6f88ab62020-11-25T01:58:53ZengSpringerOpenJournal of High Energy Physics1029-84792018-11-0120181111510.1007/JHEP11(2018)140Bootstrapping the minimal 3D SCFTAlexander Atanasov0Aaron Hillman1David Poland2Department of Physics, Yale UniversityDepartment of Physics, Yale UniversityDepartment of Physics, Yale UniversityAbstract We study the conformal bootstrap constraints for 3D conformal field theories with a ℤ 2 or parity symmetry, assuming a single relevant scalar operator ϵ that is invariant under the symmetry. When there is additionally a single relevant odd scalar σ, we map out the allowed space of dimensions and three-point couplings of such “Ising-like” CFTs. If we allow a second relevant odd scalar σ′, we identify a feature in the allowed space compatible with 3D N $$ \mathcal{N} $$ = 1 superconformal symmetry and conjecture that it corresponds to the minimal N $$ \mathcal{N} $$ = 1 supersymmetric extension of the Ising CFT. This model has appeared in previous numerical bootstrap studies, as well as in proposals for emergent supersymmetry on the boundaries of topological phases of matter. Adding further constraints from 3D N $$ \mathcal{N} $$ =1 superconformal symmetry, we isolate this theory and use the numerical bootstrap to compute the leading scaling dimensions Δ σ = Δ ϵ − 1 = .58444(22) and three-point couplings λ σσϵ = 1.0721(2) and λ ϵϵϵ = 1.67(1). We additionally place bounds on the central charge and use the extremal functional method to estimate the dimensions of the next several operators in the spectrum. Based on our results we observe the possible exact relation λ ϵϵϵ /λ σσϵ = tan(1).http://link.springer.com/article/10.1007/JHEP11(2018)140Conformal and W SymmetryConformal Field TheoryNonperturbative EffectsSupersymmetry and Duality |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Alexander Atanasov Aaron Hillman David Poland |
spellingShingle |
Alexander Atanasov Aaron Hillman David Poland Bootstrapping the minimal 3D SCFT Journal of High Energy Physics Conformal and W Symmetry Conformal Field Theory Nonperturbative Effects Supersymmetry and Duality |
author_facet |
Alexander Atanasov Aaron Hillman David Poland |
author_sort |
Alexander Atanasov |
title |
Bootstrapping the minimal 3D SCFT |
title_short |
Bootstrapping the minimal 3D SCFT |
title_full |
Bootstrapping the minimal 3D SCFT |
title_fullStr |
Bootstrapping the minimal 3D SCFT |
title_full_unstemmed |
Bootstrapping the minimal 3D SCFT |
title_sort |
bootstrapping the minimal 3d scft |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2018-11-01 |
description |
Abstract We study the conformal bootstrap constraints for 3D conformal field theories with a ℤ 2 or parity symmetry, assuming a single relevant scalar operator ϵ that is invariant under the symmetry. When there is additionally a single relevant odd scalar σ, we map out the allowed space of dimensions and three-point couplings of such “Ising-like” CFTs. If we allow a second relevant odd scalar σ′, we identify a feature in the allowed space compatible with 3D N $$ \mathcal{N} $$ = 1 superconformal symmetry and conjecture that it corresponds to the minimal N $$ \mathcal{N} $$ = 1 supersymmetric extension of the Ising CFT. This model has appeared in previous numerical bootstrap studies, as well as in proposals for emergent supersymmetry on the boundaries of topological phases of matter. Adding further constraints from 3D N $$ \mathcal{N} $$ =1 superconformal symmetry, we isolate this theory and use the numerical bootstrap to compute the leading scaling dimensions Δ σ = Δ ϵ − 1 = .58444(22) and three-point couplings λ σσϵ = 1.0721(2) and λ ϵϵϵ = 1.67(1). We additionally place bounds on the central charge and use the extremal functional method to estimate the dimensions of the next several operators in the spectrum. Based on our results we observe the possible exact relation λ ϵϵϵ /λ σσϵ = tan(1). |
topic |
Conformal and W Symmetry Conformal Field Theory Nonperturbative Effects Supersymmetry and Duality |
url |
http://link.springer.com/article/10.1007/JHEP11(2018)140 |
work_keys_str_mv |
AT alexanderatanasov bootstrappingtheminimal3dscft AT aaronhillman bootstrappingtheminimal3dscft AT davidpoland bootstrappingtheminimal3dscft |
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