Bootstrapping 3D fermions

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

Abstract

We study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge C_T. We observe features in our bounds that coincide with scaling dimensions in the GrossNeveu models at large N . We also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.

Additional Information

© 2016 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. Received: December 11, 2015. Accepted: February 17, 2016. Published: March 17, 2016. We thank Chris Beem, Shai Chester, Sheer El-Showk, Simone Giombi, Igor Klebanov, Daliang Li, Juan Maldacena, David Meltzer, Miguel Paulos, Leonardo Rastelli, Slava Rychkov, David Shih, Eva Silverstein, Andy Stergiou, Balt van Rees, and Alessandro Vichi for discussions. This work was supported by the US NSF under grant No. PHY-1418069 (LI, SSP, and RY), DOE grant number DE-SC0009988 (DSD), and NSF grant PHY-1350180 (FK and DP). DSD is supported in part by a William D. Loughlin Membership at the Institute for Advanced Study. In addition, DP, SSP, and DSD acknowledge the support of NSF Grant No. PHY-1066293 and the hospitality of the Aspen Center for Physics. We also thank the organizers and participants of the Back to the Bootstrap workshops at the University of Porto (2014) and the Weizmann Institute (2015). 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, 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_2FJHEP03_2016_120.pdf

Submitted - 1508.00012.pdf

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