Bootstrapping 3D Fermions with Global Symmetries

Creators: Iliesiu, Luca; Kos, Filip; Poland, David; Pufu, Silviu S.; Simmons-Duffin, David

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Abstract

We study the conformal bootstrap for 4-point functions of fermions 〈ψ_iψ_jψ_kψ_ℓ〉 in parity-preserving 3d CFTs, where ψ_i transforms as a vector under an O(N ) global symmetry. We compute bounds on scaling dimensions and central charges, finding features in our bounds that appear to coincide with the O(N ) symmetric Gross-Neveu-Yukawa fixed points. Our computations are in perfect agreement with the 1/N expansion at large N and allow us to make nontrivial predictions at small N . For values of N for which the Gross-Neveu-Yukawa universality classes are relevant to condensed-matter systems, we compare our results to previous analytic and numerical results.

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© 2018 The Author(s). 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: November 25, 2017; Accepted: December 21, 2017; Published: January 9, 2018. We thank Simone Giombi and Igor Klebanov for discussions, and Ran Yacoby for many discussions and collaboration in the early stages of this work. Special thanks also to Grigory Tarnopolsky for adapting the three-loop ϵ-expansion results of [33] for the GNY* model and for numerous other useful discussions. LVI and SSP are supported in part by the US NSF under grant No. PHY-1418069 and by the Simons Foundation grant No. 488653. DP is supported by NSF grant PHY-1350180 and Simons Foundation grant 488651. DSD is supported by DOE grant DE-SC0009988, a William D. Loughlin Membership at the Institute for Advanced Study, and Simons Foundation grant 488657 (Simons Collaboration on the Non-perturbative Bootstrap). The computations in this paper were run on the Feynman and Della clusters supported by Princeton University, the Omega and Grace computing clusters supported by the facilities and staff of the Yale University Faculty of Arts and Sciences High Performance Computing Center, Savio computational cluster resource provided by the Berkeley Research Computing program at the University of California Berkeley, as well as the Hyperion computing cluster supported by the School of Natural Sciences Computing Staff at the Institute for Advanced Study.

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Published - 10.1007_2FJHEP01_2018_036.pdf

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