Local Commutators and Deformations in Conformal Chiral Quantum Field Theories

Antonia M. Kukhtina, Karl-Henning Rehren
May 15, 2011
We study the general form of M"obius covariant local commutation relations in conformal chiral quantum field theories and show that they are intrinsically determined up to structure constants, which are subject to an infinite system of constraints. The deformation theory of these commutators is controlled by a cohomology complex, whose cochain spaces consist of linear maps that are subject to a complicated symmetry property, a generalization of the anti-symmetry of the Lie algebra case.