Bootstrapping mixed correlators in the 3D Ising model

Creators: Kos, Filip; Poland, David; Simmons-Duffin, David

Abstract

We study the conformal bootstrap for systems of correlators involving nonidentical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We apply this formalism to the simplest system of mixed correlators in 3D CFTs with a ℤ_2 global symmetry. For the leading ℤ_2-odd operator σ and ℤ_2-even operator ϵ, we obtain numerical constraints on the allowed dimensions (Δ_σ, Δ_ϵ) assuming that σ and ϵ are the only relevant scalars in the theory. These constraints yield a small closed region in (Δ_σ, Δ_ϵ) space compatible with the known values in the 3D Ising CFT.

Additional Information

© 2014 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: August 7, 2014. Accepted: October 27, 2014. Published: November 20, 2014. Article funded by SCOAP3. We thank Alessandro Vichi for important discussions at the initial stages of this project. We also thank Chris Beem, Alex Dahlen, Sheer El-Showk, George Fleming, Liam Fitzpatrick, Christoph Hanselka, Joanna Huey, Jared Kaplan, Zuhair Khandker, Daliang Li, Pablo Parrilo, Miguel Paulos, João Penedones, Slava Rychkov, Leonardo Rastelli, Balt van Rees, Markus Schweighofer, and Andreas Stergiou for discussions. We are grateful to Slava Rychkov for comments on the draft. We additionally thank the other organizers and participants in the Back to the Bootstrap 3 conference at CERN, and the organizers and participants of the New Nonperturbative Methods in QFT workshop at the KITP in Santa Barbara. The work of DSD is supported by DOE grant number DE-SC0009988. The work of DP and FK is supported by NSF grant 1350180. The computations in this paper were run on the Bulldog 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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