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The non-rational limit of D-series minimal models
by Sylvain Ribault
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Sylvain Ribault |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1909.10784v4 (pdf) |
| Date accepted: | 2020-07-31 |
| Date submitted: | 2020-06-23 02:00 |
| Submitted by: | Ribault, Sylvain |
| 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.
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).
Published as SciPost Phys. Core 3, 002 (2020)
Reports on this Submission
Report #1 by Anonymous (Referee 4) on 2020-7-19 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1909.10784v4, delivered 2020-07-19, doi: 10.21468/SciPost.Report.1839
Report
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.
Sylvain Ribault on 2020-06-24 [id 865]
To be more accurate: when testing crossing symmetry in Section 4.2, the sign prefactor $(-1)^{r_2s_3}$ of the three-point structure constant does appear. But this sign is not included in the definition of $\sigma(P)$ in version 4 of the submitted article. The factor $\sigma(P)$ itself is taken to be one in the $t$- and $u$-channel calculations, where it plays no role as we do not integrate over continuous momentums. In the $s$-channel calculation that factor is transformed into the distribution (4.11) by taking the limit.