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.
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Gwynne et al., Liouville Quantum Gravity with Matter Central Charge in (1, 25): A Probabilistic Approach
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- 1 2 3 Sylvain Ribault