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Bootstrapping the minimal 3D SCFT

Atanasov, Alexander and Hillman, Aaron and Poland, David (2018) Bootstrapping the minimal 3D SCFT. Journal of High Energy Physics, 2018 (11). Art. No. 140. ISSN 1126-6708. doi:10.1007/JHEP11(2018)140.

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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 NN = 1 superconformal symmetry and conjecture that it corresponds to the minimal NN = 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 NN =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).

Item Type:Article
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URLURL TypeDescription Paper
Poland, David0000-0003-3854-2430
Additional Information:© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: August 8, 2018; Revised: October 26, 2018; Accepted: November 10, 2018; Published: November 22, 2018. We would like to thank Soner Albayrak, Luca Iliesiu, Filip Kos, Daliang Li, David Meltzer, Silviu Pufu, Slava Rychkov, Michael Scherer, and David Simmons-Duffin for relevant discussions. We thank the organizers of the Bootstrap 2018 workshop where a portion of this work was completed. This research is supported by NSF grant PHY-1350180 and Simons Foundation grant 488651 (Simons Collaboration on the Nonperturbative Bootstrap). The computations in this paper were run on the Grace computing cluster supported by the facilities and staff of the Yale University Faculty of Arts and Sciences High Performance Computing Center.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons Foundation488651
Subject Keywords:Conformal and W Symmetry; Conformal Field Theory; Nonperturbative Effects; Supersymmetry and Duality
Issue or Number:11
Record Number:CaltechAUTHORS:20181126-084412286
Persistent URL:
Official Citation:Atanasov, A., Hillman, A. & Poland, D. J. High Energ. Phys. (2018) 2018: 140.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91150
Deposited By: Tony Diaz
Deposited On:26 Nov 2018 17:42
Last Modified:16 Nov 2021 03:38

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