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Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry
by Johan Henriksson, Andreas Stergiou
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Johan Henriksson · Andreas Stergiou |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2101.08788v2 (pdf) |
| Date accepted: | 2021-07-06 |
| Date submitted: | 2021-06-03 17:54 |
| Submitted by: | Henriksson, Johan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Fixed points in three dimensions described by conformal field theories with $MN_{m,n}= O(m)^n\rtimes S_n$ global symmetry have extensive applications in critical phenomena. Associated experimental data for $m=n=2$ suggest the existence of two non-trivial fixed points, while the $\varepsilon$ expansion predicts only one, resulting in a puzzling state of affairs. A recent numerical conformal bootstrap study has found two kinks for small values of the parameters $m$ and $n$, with critical exponents in good agreement with experimental determinations in the $m=n=2$ case. In this paper we investigate the fate of the corresponding fixed points as we vary the parameters $m$ and $n$. We find that one family of kinks approaches a perturbative limit as $m$ increases, and using large spin perturbation theory we construct a large $m$ expansion that fits well with the numerical data. This new expansion, akin to the large $N$ expansion of critical $O(N)$ models, is compatible with the fixed point found in the $\varepsilon$ expansion. For the other family of kinks, we find that it persists only for $n=2$, where for large $m$ it approaches a non-perturbative limit with $\Delta_\phi\approx 0.75$. We investigate the spectrum in the case $MN_{100,2}$ and find consistency with expectations from the lightcone bootstrap.
Author comments upon resubmission
List of changes
Introduction: Added some further clarifications and references (including the new footnote 3) concerning the literature discussion of non-perturbative fixed-points, and added some literature values for these. Clarified some formulations relating to the numerical bootstrap (regarding what a kink signals and numerical precision).
Table 2. Added a dashed line to separate experimental and MC data from kink 1 results. Added a new reference with additional MC result.
Figure 4. Added precision for qboot computations.
Section 4. Fixed typo. Clarified what we mean by a simplifying limit and that the cartoons in figure 8 need to be confirmed or disproved by further studies.
Published as SciPost Phys. 11, 015 (2021)
Reports on this Submission
Report #1 by Anonymous (Referee 3) on 2021-6-18 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2101.08788v2, delivered 2021-06-18, doi: 10.21468/SciPost.Report.3033
Report
I thank the authors for their careful replies, and I appreciate the authors being conservative in the estimates even though the shown plots would suggest quite smaller error bars. The authors have addressed all my points, and I am happy to recommend the paper for publication. It can be published as is, although I have one minor final clarification to ask. Indeed eqs. (3.6-3.8) do not suggest a large spin expansion, the cause of confusion is the statement above (3.3) where it seems to say the dDisc is computed in the limit $v \ll 0$, and since the section is called large spin perturbation theory it was also not clear if non-perturbative finite spin effects were taken into account. (I am not sure [29,30] were what the authors meant to refer to in their reply.) For the paper to be self-contained, could the authors just briefly comment down to which spin they expect the inversion formula to give the correct answer, and thus their results to hold? In a generic CFT it would be for $\ell>1$, however the correlator being inverted here is an expansion for large $m$ - is the Regge growth expected to be the same for the $\mathcal{O}(m^{-1})$ piece of the correlator, or assumed to be? Or is it even better, since below (3.8) the results are evaluated for $\ell=1$? This issue is commented upon when discussing the $\ell=0$ evaluation of the authors' results but I believe it would be beneficial to comment a little bit earlier.