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The non-rational limit of D-series minimal models
by Sylvain Ribault
- Published as SciPost Phys. Core 3, 002 (2020)
|As Contributors:||Sylvain Ribault|
|Arxiv Link:||https://arxiv.org/abs/1909.10784v4 (pdf)|
|Date submitted:||2020-06-23 02:00|
|Submitted by:||Ribault, Sylvain|
|Submitted to:||SciPost Physics Core|
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.
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Published as SciPost Phys. Core 3, 002 (2020)
Author comments upon resubmission
Let me emphasize that only the $P$-dependence of $\sigma(P)$ matters for taking the limit of a given four-point function. And $\sigma(P)$ does not appear in the numerical tests of crossing symmetry in Section 4.2, as taking the continuum limit transforms $\sigma(P)$ into the distribution (4.11).
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 1 on 2020-7-19 Invited Report
- Cite as: Anonymous, Report on arXiv:1909.10784v4, delivered 2020-07-19, doi: 10.21468/SciPost.Report.1839
I would like yet again to thank the author for clarifying the results in this paper. I still find the ultimate analysis unconvincing, but the calculations presented are still very interesting and are now sufficiently detailed to allow a reader to repeat the derivations and decide for themselves whether there is an alternative explanation, and I am happy to recommend publication.