Local Commutators and Deformations in Conformal Chiral Quantum Field Theories

TL;DR

This paper investigates the structure and deformation of local commutation relations in conformal chiral quantum field theories, revealing their dependence on structure constants constrained by a complex cohomology framework.

Contribution

It introduces a cohomology-based approach to analyze the deformation theory of local commutators in conformal chiral QFTs, generalizing Lie algebra concepts.

Findings

Local commutation relations are determined up to structure constants.

Deformation theory is governed by a specialized cohomology complex.

Constraints on structure constants form an infinite system.

Abstract

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.