Defects via Factorization Algebras

TL;DR

This paper develops a mathematical framework for describing defects in field theories using factorization algebras and the BV formalism, integrating recent advances on boundary conditions.

Contribution

It introduces a novel formulation of defects in field theories via factorization algebras, connecting boundary conditions with the BV formalism and recent boundary work.

Findings

Framework successfully models various natural defect examples

Integrates recent boundary condition research into defect theory

Provides a rigorous mathematical description of defects

Abstract

We provide a mathematical formulation of the idea of a defect for a field theory, in terms of the factorization algebra of observables and using the BV formalism. Our approach follows a well-known ansatz identifying a defect as a boundary condition along the boundary of a blow-up, but it uses recent work of Butson-Yoo and Rabinovich on boundary conditions and their associated factorization algebras to implement the ansatz. We describe how a range of natural examples of defects fits into our framework.