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Infinite conformal symmetry in two-dimensional quantum field theory. (English) Zbl 0661.17013
We present an investigation of the massless, two-dimensional, interacting field theories. Their basic property is their invariance under an infinite-dimensional group of conformal (analytic) transformations. It is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the Virasoro algebra, and that the correlation functions are built up of the ‘conformal blocks’ which are completely determined by the conformal invariance. Exactly solvable conformal theories associated with the degenerate representations are analyzed. In these theories the anomalous dimensions are known exactly and the correlation functions satisfy systems of linear differential equations.

MSC:
17B65Infinite-dimensional Lie (super)algebras
81T40Two-dimensional field theories, conformal field theories, etc.
58J90Applications of PDE on manifolds
17B10Representations of Lie algebras, algebraic theory
81R10Infinite-dimensional groups and algebras motivated by physics