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On 2d CFTs that interpolate between 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/1809.03722v2 (pdf) |
| Date submitted: | 2018-12-05 01:00 |
| Submitted by: | Ribault, Sylvain |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 2) on 2019-4-30 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1809.03722v2, delivered 2019-04-29, doi: 10.21468/SciPost.Report.924
Strengths
A new approach to finding the most general extension of minimal CFTs at rational values of the central charge, by considering limits of the generic central charges.
Weaknesses
The logic of the paper is slightly complicated and difficult to follow, and the conclusions not easy to draw.
It would be interesting to study a particular case in detail and be able to make more definite statements.
Report
The subject of the paper is the study of two dimensional conformal field theories at arbitrary values of central charge and at the limiting value when the central charges become rational, the purpose being to understand how the minimal models, or generalised minimal models, can be obtained from generic conformal field theories. The study is based on the analytic structure of the four point functions.
The parameter of interest is the dimension of the fields in the intermediate channel; according to a representation due to Zamolodchikov, the four point function as a function of this variable has poles at all the values corresponding to the degenerate fields.
It is the position and the multiplicity of these poles that is the focus of the present work, namely how do they combine in the limit of rational central charge.
The first observation is that for generic charges of the four operators, the Zamolodchikov’s
representation superficially diverges in the rational limit; however the superficial divergences cancel between different terms. The mechanism is illustrated in a simple case, where the simple poles become double poles after the cancelation of divergences - but no general proof is given.
The remaining statements are a couple of conjectures concerning the behaviour of the conformal blocks when the charges of the four external fields are degenerate and the internal dimension approaches the value of a degenerate field allowed or not by the fusion rules.
The results are not extremely conclusive, but the paper is presumably the beginning a systematic study of the rational limit of generic CFTs.
Requested changes
Concerning te structure of the paper
1. it would be useful to summarise the results in the introduction,
and try to keep the paper self-contained (e.g. define a non-diagonal CFT).
2. it would be helpful to explain if the summation indexing (2.28) is continuous or discrete, and what happens to this representation for the minimal models.
I would suggest also:
3. to use a figure caption for the figure on page 8,
4. to use the standard plural for the late words (e.g momentums -> momenta)
5. to use the standard form for the references (i.e. with the journal number).