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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
| Authors (as registered SciPost users): | Johan Henriksson · Stefanos Robert Kousvos · Andreas Stergiou |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2004.14388v3 (pdf) |
| Date accepted: | Sept. 4, 2020 |
| Date submitted: | Aug. 26, 2020, 8:43 p.m. |
| Submitted by: | Andreas Stergiou |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
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.
Author comments upon resubmission
List of changes
- 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.
- 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.
- We added footnote 1 to address Requested Change 2 in Report 2.
- We added footnote 17 to address Requested Change 3 in Report 2.
Published as SciPost Phys. 9, 035 (2020)