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The nonrational limit of Dseries minimal models
by Sylvain Ribault
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Submission summary
Authors (as registered SciPost users):  Sylvain Ribault 
Submission information  

Preprint Link:  https://arxiv.org/abs/1909.10784v1 (pdf) 
Date submitted:  20191022 02:00 
Submitted by:  Ribault, Sylvain 
Submitted to:  SciPost Physics Core 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We study the limit of Dseries minimal models when the central charge tends to a generic irrational value $c\in (\infty, 1)$. We find that the limit theory's diagonal threepoint structure constant differs from that of Liouville theory by a distribution factor, which is given by a divergent Verlinde formula. Nevertheless, correlation functions that involve both nondiagonal and diagonal fields are smooth functions of the diagonal fields' conformal dimensions. The limit theory is a nontrivial example of a nondiagonal, nonrational, solved twodimensional conformal field theory.
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Reports on this Submission
Anonymous Report 1 on 20191216 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1909.10784v1, delivered 20191216, doi: 10.21468/SciPost.Report.1395
Strengths
1 The paper makes a serious attempt to understand the limit(s) of the Dseries minimal models. Not all the results are rigorous, but I did not find any mistakes.
Weaknesses
1 The analysis depends strongly on the fields being clearly divided into diagonal and nondiagonal, but the "nondiagonal" sector includes diagonal fields of the sort $(r,s),(r,s) = (0,s),(0,s)$. This means that further analysis is required to justify equations (2.16), (2.18), (2.19) etc. I think this could be done, for example it is noted before equation (2.27) that these can be distinguished by their 3 point functions, but at the very least the words "nondiagonal sector" are misleading. This needs to be explained clearly.
2 I though the discussion in in the conclusion was a little disingenuous. The Dseries diagonal fields have an identical set of structure constants and correlation functions with a subset of the Aseries models, but the Aseries models have extra diagonal fields and so it is not especially surprising if the structure constants of the limits are different.
3 I do not know in what sense the degenerate fields "exist" in the theory if they are excluded from the spectrum. They are outside the theory and I would like some justification why they should be able to be included consistently and that deductions from their correlation functions are still valid.
Report
This is an interesting paper adding to the study of limit CFTs and CFTs with continuous spectrum. There are some clear issues involved with defining the limit CFT(s) of the Dmodels which are discussed and tackled.
I would have liked a clearer demonstrations that there are in fact two different CFTs in the limit, one from $\beta$ and one from $1/\beta$. It is asserted a couple of times but I did not find a clear explanation: apologies if I just missed it.
Requested changes
1 please clarify that the "nondiagonal sector" also includes diagonal fields and that the restrictions on fusion rules etc follow from other considerations than "diagonality".