Factorization Algebras in Quantum Field Theory

Over two volumes, the authors develop factorization algebras, creating an essential reference for graduates and researchers.

Ideal for researchers and graduate students at the interface between mathematics and physics, this two-volume set discusses factorization algebras. The first volume highlights examples exhibiting their use in field theory, while the second develops quantum field theory from the ground up using a rich mix of modern mathematics.Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In the first volume of this set, the authors develop the theory of factorization algebras in depth, with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern–Simons theory. In the second volume, they show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies.