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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
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Submission summary
| Authors (as registered SciPost users): | Johan Henriksson · Stefanos Robert Kousvos · Andreas Stergiou |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2004.14388v2 (pdf) |
| Date submitted: | 2020-06-15 02:00 |
| Submitted by: | Stergiou, Andreas |
| 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.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2020-8-12 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2004.14388v2, delivered 2020-08-12, doi: 10.21468/SciPost.Report.1910
Strengths
- contains several details which make possible to reproduce most of the analytic results without much work
- mixed correlator approach
- synergy between analytic and numerical approaches
Weaknesses
- not clearly specified the results, in some places they appear to be hidden by technical details
Report
The paper is overall clearly written and contains several interesting results. I have a list of suggestions/questions that I would like the authors to address before the paper can be accepted for publication by SciPost.
Requested changes
1-in the last paragraph before 1.1, it is mentioned that m is small and n is large. Is it enough that m is smaller (even much smaller) than m or not?
2- there are two expansions made, the small $\epsilon$ and the large $n$ expansion. Specially in the introduction, it is not clear which is the order of the expansions. Is there any issue related to it?
3-regarding the non unitarity: how would you have expected to see it? As it is pointed out in the paper, the numerical bootstrap only finds bounds or islands of theories which are unitary so it is not clear how the non unitarity would be signalled both in the numerical and analytic approaches.
Report #1 by Anonymous (Referee 2) on 2020-7-26 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2004.14388v2, delivered 2020-07-26, doi: 10.21468/SciPost.Report.1861
Strengths
1) Detailed discussion of the results.
2) The presentation is very balanced: the reliability of the results is always discussed clearly and honestly.
Weaknesses
1) Too long. It would have been probably better to have different papers for the large N behavior and
for the O(2)timesO(2) and O(2)times O(3) behavior
Report
I think the paper should be published. The paper studies a class of models that have been of great interest in the last 30 years. Nonetheless, the critical
behavior in the physically interesting cases is still debated. Thus, I have no reservations on its significance. Moreover, the paper is clearly written (I have a few comments to improve the presentation).
Requested changes
Given the length of the paper it would be interesting to summarize the results for the two physically interesting cases O(2)timesO(3) and O(2)timesO(2) in a table in the conclusions. One should report the results using the standard notation using the in statistical physics (exponents nu, eta, omega, crossover exponents phi), comparing them with the literature results . This would allow workers in statistical and condensed matter to grab the results without the need of looking inside the full article and of understanding the notations used in the conformal bootstrap method.