Boundaries, defects and Frobenius algebras

TL;DR

This paper explores the mathematical structures underlying boundary conditions, defects, and D-branes in conformal field theories, using topological and algebraic tools to enhance understanding and computational methods.

Contribution

It introduces a new framework combining topological field theory and non-commutative algebra in tensor categories to analyze boundary conditions, defect lines, and disorder fields in CFT.

Findings

Developed a method to construct CFT correlators using tensor categories.

Unified treatment of boundary conditions, defect lines, and disorder fields.

Enhanced computational tools for analyzing boundary phenomena in CFT.

Abstract

The interpretation of D-branes in terms of open strings has lead to much interest in boundary conditions of two-dimensional conformal field theories (CFTs). These studies have deepened our understanding of CFT and allowed us to develop new computational tools. The construction of CFT correlators based on combining tools from topological field theory and non-commutative algebra in tensor categories, which we summarize in this contribution, allows e.g. to discuss, apart from boundary conditions, also defect lines and disorder fields.