Configuration space integrals and index theory

Abstract: We explain a geometric formulation of the low energy effective theory of sigma models in terms of bundles of factorization algebras. Appropriate regularization for Integrals over configuration spaces arises naturally from quantum field theories and will in general give rise to index type theories. As a case study in dimension two,  we introduce a geometric renormalization method for regularized integrals over configuration spaces of Riemann surfaces in 2d chiral quantum field theory. It provides a mathematical tool to formulate correlation functions of non-local operators in a chiral CFT that will lead to an algebraic analogue of elliptic index theory.

Mathematics

Audience: researchers in the topic

ICCM 2020