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Bootstrapping MN and Tetragonal CFTs in Three Dimensions
by Andreas Stergiou
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|Authors (as registered SciPost users):||Andreas Stergiou|
|Preprint Link:||https://arxiv.org/abs/1904.00017v1 (pdf)|
|Date submitted:||2019-04-08 02:00|
|Submitted by:||Stergiou, Andreas|
|Submitted to:||SciPost Physics|
Conformal field theories (CFTs) with MN and tetragonal global symmetry in $d=2+1$ dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions. As a result, they have been studied in great detail with the $\varepsilon=4-d$ expansion and other field theory methods. The study of these theories with the nonperturbative numerical conformal bootstrap is initiated in this work. Bounds for operator dimensions are obtained and they are found to possess sharp kinks in the MN case, suggesting the existence of full-fledged CFTs. Based on the existence of a certain large-$N$ expansion in theories with MN symmetry, these are argued to be the CFTs predicted by the $\varepsilon$ expansion. In the tetragonal case no new kinks are found, consistently with the absence of such CFTs in the $\varepsilon$ expansion. Estimates for critical exponents are provided for a few cases describing phase transitions in actual physical systems. In two particular MN cases, corresponding to theories with global symmetry groups $O(2)^2\rtimes S_2$ and $O(2)^3\rtimes S_3$, a second kink is found. In the $O(2)^2\rtimes S_2$ case it is argued to be saturated by a CFT that belongs to a new universality class relevant for the structural phase transition of NbO$_2$ and paramagnetic-helimagnetic transitions of the rare-earth metals Ho and Dy. In the $O(2)^3\rtimes S_3$ case it is suggested that the CFT that saturates the second kink belongs to a new universality class relevant for the paramagnetic-antiferromagnetic phase transition of the rare-earth metal Nd.
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- Cite as: Anonymous, Report on arXiv:1904.00017v1, delivered 2019-05-29, doi: 10.21468/SciPost.Report.980
1-is well written and clear
2-addresses a very interesting problem
3-clarifies some discrepancies, observed in the literature
4-has potential connection with experiments
1- Parts of the paper are very technical
2-Quite difficult to be accessed by non experts
This paper addresses an interesting problem which is the application of numerical bootstrap techniques to conformal field theories with specific global symmetry gauge groups (semidirect products of $K^n \rtimes S_n$). Such cases are interesting both because beside the $\epsilon$ expansion there are no other methods to study these theories and also because they are central in the description of phase transitions in helimagnets and antiferromagnets. The paper shed light on the existence of such theories in three dimensions and on the values of critical exponents, for some specific theories. The results are quite robust and promising, despite the fact that it is the first time that numerical conformal bootstrap techniques are applied to these systems. This paper deserves the publication, after few points have been clarified (see section ''requested changes'')
1- I think it would be better if the author reports also the experimental data in a table, which could be displayed in the introduction.
2-It is not very clear to me the contradiction with refs [18,12] of the paper's reference list discussed in one of the last paragraphs of the introduction. Would it be possible that the CFT that saturates the bound is just different? meaning has one critical exponent which is the same (what is denoted by $\nu$) but not the other ($\beta$)?
3- It would be better to improve readability to have some of the details of sec 2.1 and 4.1 in an appendix