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Analytic and Numerical Bootstrap of CFTs with $O(m)\times O(n)$ Global Symmetry in 3D

by Johan Henriksson, Stefanos R. Kousvos, Andreas Stergiou

Submission summary

As Contributors: Andreas Stergiou
Arxiv Link: (pdf)
Date accepted: 2020-09-04
Date submitted: 2020-08-26 20:43
Submitted by: Stergiou, Andreas
Submitted to: SciPost Physics
Discipline: Physics
Subject area: High-Energy Physics - Theory
Approaches: Theoretical, Computational


Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with $O(m)\times O(n)$ global symmetry in $d=3$ spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in $\varepsilon=4-d$ and in $1/n$, with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for $O(2)\times O(n)$ theories for various values of $n$. Some of these islands can be attributed to fixed points predicted by perturbative methods like the $\varepsilon$ and large-$n$ expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.

Ontology / Topics

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Conformal bootstrap Conformal field theory (CFT) Global symmetries

Published as SciPost Phys. 9, 035 (2020)

Author comments upon resubmission

We would like to thank both referees for their comments on our manuscript. A list of changes to address the referees' comments can be found below.

List of changes

1. We added tables with results for critical exponents in our conclusion section, as suggested in Report 1. Hopefully this also ameliorates the indicated weakness in Report 2.
2. In response to Requested Change 1 in Report 2, we emphasize that our expansion parameter is 1/n, not m/n. This is clearly stated in the paragraph before subsection 1.2.
3. We added footnote 1 to address Requested Change 2 in Report 2.
4. We added footnote 17 to address Requested Change 3 in Report 2.

Submission & Refereeing History

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Resubmission 2004.14388v3 on 26 August 2020

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