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arXiv · 2301.04143

Topological defects as lagrangian correspondences

Alex S. Arvanitakis
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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.

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Alex S. Arvanitakis. 2023-01-10. Topological defects as lagrangian correspondences. https://doi.org/10.1103/physrevd.107.066016

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