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Non-Invertible Defects in Nonlinear Sigma Models and Coupling to Topological Orders

Po-Shen Hsin
Dec 2022
摘要
Nonlinear sigma models appear in a wide variety of physics contexts, such asthe long-range order with spontaneously broken continuous global symmetries.There are also large classes of quantum criticality admit sigma modeldescriptions in their phase diagrams without known UV complete quantum fieldtheory descriptions. We investigate defects in general nonlinear sigma modelsin any spacetime dimensions, which include the ``electric" defects that arecharacterized by topological interactions on the defects, and the ``magnetic"defects that are characterized by the isometries and homotopy groups. We use ananalogue of the charge-flux attachment to show that the magnetic defects are ingeneral non-invertible, and the electric and magnetic defects form junctionsthat combine defects of different dimensions into analogues of higher-groupsymmetry. We explore generalizations that couple nonlinear sigma models totopological quantum field theories (TQFT) by defect attachment, which modifiesthe non-invertible fusion and braiding of the defects. We discuss severalapplications, including constraints on energy scales and scenarios of lowenergy dynamics with spontaneously symmetry breaking in gauge theories, andaxion gauge theories.
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