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Minimal lectures on twodimensional conformal field theory
by Sylvain Ribault
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Submission summary
Authors (as registered SciPost users):  Sylvain Ribault 
Submission information  

Preprint Link:  http://arxiv.org/abs/1609.09523v4 (pdf) 
Date accepted:  20180118 
Date submitted:  20180115 01:00 
Submitted by:  Ribault, Sylvain 
Submitted to:  SciPost Physics Lecture Notes 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We provide a brief but selfcontained 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 fourpoint 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:
1. 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.
2. 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.
3. 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.
4. 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:
1. 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.
2. In Exercise 3.5, I have added substantial hints.
Published as SciPost Phys. Lect. Notes 1 (2018)