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Conformal field theory on the plane
Sylvain Ribault
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We review conformal field theory on the plane in the conformal bootstrap approach. We introduce the main ideas of the bootstrap approach to quantum field theory, and how they apply to two-dimensional theories with local conformal symmetry. We describe the mathematical structures that appear in such theories, from the Virasoro algebra and its representations, to BPZ equations and conformal blocks. Examples include Liouville theory, (generalized) minimal models, free bosonic theories, the H₃^+ model, and the SU₂ and SL₂(ℝ) WZW models. We also discuss relations between some of these models, and limits of these models when the central charge and/or conformal dimensions tend to particular values.
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