Deformations of Quantum Field Theories

Eli Hawkins (U of York)

Sep 03. 2020, 16:15 — 17:00

An algebraic quantum field theory is in particular a diagram of algebras – i.e., a functor from a small category to a category of algebras. To first order, the deformations and symmetries of a diagram of algebras are described by its asimplicial Hochschild cohomology. I have constructed an operad, Quilt, that describes natural operations on the Hochschild bicomplex of a diagram of algebras, and used this to describe the Gerstenhaber algebra structure of the cohomology. I have further used Quilt to construct an L-infinity algebra structure on the bicomplex itself. This determines a (generalized) Maurer-Cartan equation, the solutions of which are precisely the finite deformations of the diagram of algebras.

These structures may form the basis for a general theory of deformations of algebraic quantum field theories, along the lines of Kontsevich’s work on formality and deformation quantization.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures and Field Theory - partially postponed (Thematic Programme)
Anton Alekseev (U Genève)
Stefan Fredenhagen (U of Vienna)
Nicolai Reshetikhin (UC, Berkeley)
Thomas Strobl (U Lyon)
Chenchang Zhu (U Göttingen)