Minimal lectures on two-dimensional conformal field theory

Sylvain Ribault (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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 Liouville theory and minimal models 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.

Domains: Mathematical Physics [math-ph]

Sylvain Ribault. Minimal lectures on two-dimensional conformal field theory. SciPost Physics, 2018, 1, ⟨10.21468/SciPostPhysLectNotes.1⟩. ⟨cea-01469008⟩