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The non-rational limit of D-series minimal models
by Sylvain Ribault
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Sylvain Ribault |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1909.10784v1 (pdf) |
| Date submitted: | Oct. 22, 2019, 2 a.m. |
| Submitted by: | Sylvain Ribault |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study the limit of D-series minimal models when the central charge tends to a generic irrational value $c\in (-\infty, 1)$. We find that the limit theory's diagonal three-point 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 non-diagonal and diagonal fields are smooth functions of the diagonal fields' conformal dimensions. The limit theory is a non-trivial example of a non-diagonal, non-rational, solved two-dimensional conformal field theory.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2019-12-16 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1909.10784v1, delivered 2019-12-16, doi: 10.21468/SciPost.Report.1395
Strengths
1- The paper makes a serious attempt to understand the limit(s) of the D-series 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 non-diagonal, but the "non-diagonal" 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 "non-diagonal sector" are misleading. This needs to be explained clearly.
2- I though the discussion in in the conclusion was a little disingenuous. The D-series diagonal fields have an identical set of structure constants and correlation functions with a subset of the A-series models, but the A-series 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
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 "non-diagonal sector" also includes diagonal fields and that the restrictions on fusion rules etc follow from other considerations than "diagonality".