Topological defects as lagrangian correspondences

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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.
Original languageEnglish
Article number066016
Number of pages6
JournalPhys. Rev. D
Volume107
Issue number6
DOIs
Publication statusPublished - 15 Mar 2023

Bibliographical note

5+1 pages v2: fixed Acknowledgments, v3: fixed a typo; essentially matches published version

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