SciPost Submission Page
Minimal lectures on two-dimensional conformal field theory
by Sylvain Ribault
Submission summary
| Authors (as registered SciPost users): | Sylvain Ribault |
| Submission information | |
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| Preprint Link: | http://arxiv.org/abs/1609.09523v4 (pdf) |
| Date accepted: | Jan. 18, 2018 |
| Date submitted: | Jan. 15, 2018, 1 a.m. |
| Submitted by: | Sylvain Ribault |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We provide a brief but self-contained review of conformal field theory on the Riemann sphere. We first introduce general axioms such as local conformal invariance, and derive Ward identities and BPZ equations. We then define minimal models and Liouville theory by specific axioms on their spectrums and degenerate fields. We solve these theories by computing three- and four-point functions, and discuss their existence and uniqueness.
Author comments upon resubmission
List of changes
Reply to Reviewer 1: The typo after (3.15) is now corrected.
Reply to Reviewer 3:
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There was indeed a contradition because Axiom 3.4 was too strong. I have modified that Axiom so that it applies only to fields that correspond to states in the spectrum. Then OPEs of degenerate fields are not covered, and should be discussed separately. I have added such a discussion after Axiom 4.10.
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I have added a paragraph at the very end of Section 5, in order to make contact with the original definition (and naming) of Liouville theory, and to refer the reader to ref. [3] for more details.
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I have added a paragraph between eqs. (4.10) and (4.11) in order to further discuss the guess for the lower bound, and to mention the alternative guess that the lower bound could be zero.
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Between eqs. (5.18) and (5.19), I have amended the discussion of invariance under field renormalization: it is now stated that invariant quantities are sufficient for checking crossing symmetry, and explained why we may want to choose a normalization.
Additional changes:
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At the end of the introduction, I have added a further motivation for the minimalistic approach, namely that it can be useful in research on other CFTs. Reference [6] is given as an example.
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In Exercise 3.5, I have added substantial hints.
Published as SciPost Phys. Lect. Notes 1 (2018)