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Published November 2015 | Published + Submitted
Journal Article Open

Bootstrapping the O(N) archipelago


We study 3d CFTs with an O(N) global symmetry using the conformal bootstrap for a system of mixed correlators. Specifically, we consider all nonvanishing scalar four-point functions containing the lowest dimension O(N) vector ϕi and the lowest dimension O(N) singlet s, assumed to be the only relevant operators in their symmetry representations. The constraints of crossing symmetry and unitarity for these four-point functions force the scaling dimensions (Δ_ϕ, Δ_s) to lie inside small islands. We also make rigorous determinations of current two-point functions in the O(2) and O(3) models, with applications to transport in condensed matter systems.

Additional Information

© 2015 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 20, 2015. Accepted: October 8, 2015. Published: November 17, 2015. Article funded by SCOAP3. We thank Chris Beem, Sheer El-Showk, Luca Iliesiu, Emanuel Katz, Igor Klebanov, Daliang Li, Miguel Paulos, Silviu Pufu, Leonardo Rastelli, Slava Rychkov, Subir Sachdev, Erik Sørensen, Andreas Stergiou, Balt van Rees, William Witczak-Krempa, and Ran Yacoby for discussions. We additionally thank the organizers of the PCTS workshop "Higher Spin Symmetries and Conformal Bootstrap" for facilitating discussions related to this work. The work of DSD is supported by DOE grant number DE-SC0009988 and a William D. Loughlin Membership at the Institute for Advanced Study. 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, on the Hyperion computing cluster supported by the School of Natural Sciences Computing Staff at the Institute for Advanced Study and on the CERN cluster.

Attached Files

Published - 10.1007_2FJHEP11_2015_106.pdf

Submitted - 1504.07997.pdf


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August 20, 2023
August 20, 2023