SciPost Submission Page
The nonrational limit of Dseries minimal models
by Sylvain Ribault
This Submission thread is now published as
Submission summary
Authors (as registered SciPost users):  Sylvain Ribault 
Submission information  

Preprint Link:  https://arxiv.org/abs/1909.10784v4 (pdf) 
Date accepted:  20200731 
Date submitted:  20200623 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.
Author comments upon resubmission
Let me emphasize that only the $P$dependence of $\sigma(P)$ matters for taking the limit of a given fourpoint 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
Anonymous Report 1 on 2020719 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1909.10784v4, delivered 20200719, 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 20200624 [id 865]
To be more accurate: when testing crossing symmetry in Section 4.2, the sign prefactor $(1)^{r_2s_3}$ of the threepoint 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.