Conformal field theory

Summary

A conformal field theory is a quantum field theory that is invariant under conformal maps, the transformations that preserve angles but may change lengths. Such theories have no intrinsic length scale, and they describe critical points of statistical systems and fixed points of the renormalization group. In dimension at least three the conformal group is finite-dimensional, but in dimension two the local conformal maps form an infinite-dimensional family. There the Virasoro algebra makes many theories exactly solvable. Conformal field theory is central to string theory, to the theory of vertex operator algebras, and to the AdS/CFT correspondence.