Topological defects as Lagrangian correspondences

Abstract

Topological defects attract much recent interest in high-energy and condensed matter physics, because they encode (noninvertible) 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.