Topological defects as lagrangian correspondences

TL;DR

This paper models topological defects as Lagrangian correspondences within the Weinstein symplectic category, providing a geometric framework for understanding defect fusion and dualities in string theory.

Contribution

It introduces a novel geometric approach to topological defects using Lagrangian correspondences and applies this to construct duality defects, including a new non-abelian T-duality defect.

Findings

Defects are represented as Lagrangian correspondences.

Defect fusion corresponds to geometric composition.

Constructed new T-duality defect with topology change.

Abstract

Topological defects attract much recent interest in high-energy and condensed matter physics because they encode (non-invertible) symmetries and dualities. We study codimension-1 topological defects from a hamiltonian point of view, with the defect location playing the role of `time'. We show that the Weinstein symplectic category governs topological defects and their fusion: each defect is a lagrangian correspondence, and defect fusion is their geometric composition. We illustrate the utility of these ideas by constructing S- and T-duality defects in string theory, including a novel topology-changing non-abelian T-duality defect.