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Bootstrapping Mixed Correlators in ThreeDimensional Cubic Theories
by Stefanos R. Kousvos, Andreas Stergiou
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Submission summary
As Contributors:  Stefanos Robert Kousvos · Andreas Stergiou 
Arxiv Link:  https://arxiv.org/abs/1810.10015v3 (pdf) 
Date accepted:  20190315 
Date submitted:  20181129 01:00 
Submitted by:  Stergiou, Andreas 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
Threedimensional theories with cubic symmetry are studied using the machinery of the numerical conformal bootstrap. Crossing symmetry and unitarity are imposed on a set of mixed correlators, and various aspects of the parameter space are probed for consistency. An isolated allowed region in parameter space is found under certain assumptions involving pushing operator dimensions above marginality, indicating the existence of a conformal field theory in this region. The obtained results have possible applications for ferromagnetic phase transitions as well as structural phase transitions in crystals. They are in tension with previous $\varepsilon$ expansion results, as noticed already in earlier work.
Ontology / Topics
See full Ontology or Topics database.Published as SciPost Phys. 6, 035 (2019)
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 1 on 2019220 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1810.10015v3, delivered 20190220, doi: 10.21468/SciPost.Report.837
Strengths
1. The paper contains significant, possibly groundbreaking results.
2. The paper is very clearly written.
Weaknesses
1. If I had to give one I would say that since the paper is a straightforward application of existing methodology, to compensate for this perhaps more space could have been given to reviewing and discussing existing literature on fixed points with cubic symmetry.
Report
This is a sharp, to the point, nice paper applying conformal bootstrap methods to uncover properties of possible fixed points with cubic symmetry. The main result is the discovery of an island in the space of allowed theories, which suggests the possible existence of a new, hitherto unnoticed CFT with cubic symmetry, dubbed "Platonic CFT". Numeric results seem to be in agreement with measurements of critical exponents for certain structural phase transitions.
I have a few very minor comments given below.
Requested changes
1. Could the authors clarify (for completeness) what is meant by the decoupled Ising model.
2. The long sentence starting just above 1.2 and finishing after 1.3 could be improved a bit in clarity.
3. In 2.1, it's a bit odd at first to say that $\phi_i$ lives in the offdiagonal irrep when this has just been explained as coming from a piece of the symmetric traceless tensor, in the sense that one expects that $\phi_i$ should be coming from the fundamental of O(3). I'm guessing the fundamental of O(3) turns out to transform in the same irrep thanks to eqn. 2.3? If so, might be worth making this more explicit.
4. In 2.7, it is not obvious what irrep $Y'_l$ belongs to, given the notation up to that point. Perhaps the Z in 2.3 could be changed to a Y with a single index, or the Y in 2.7 could be changed to a Z?
5. It would be important for the authors to comment on the dependence of their numerical results on the gap assumption on $\phi'$.
6. It would be useful, if possible, to place the epsexpansion cubic fixed point on the exclusion plots.
Author: Andreas Stergiou on 20190307 [id 461]
(in reply to Report 1 on 20190220)We thank the referee for his/her suggestions. To address the referee's requested changes we have made the following additions/clarifications (please see v4 of our manuscript at https://arxiv.org/abs/1810.10015v4):
Hopefully our last amendment also helps the reader make contact with existing literature of the $\varepsilon$ expansion in theories with cubic symmetry.