Topological defects from higher gauging are shown, via explicit Lagrangian computations, to satisfy the Karoubi completeness condition of Johnson-Freyd's higher fusion categories, and this is identified with splitting into gauging interfaces.
On the Higher Categorical Structure of Topological Defects in Quantum Field Theories
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abstract
We propose a unifying mathematical framework describing the higher categorical structures formed by topological defects in quantum field theory equipped with tangential structures, such as orientations, framings, or $\operatorname{Pin}^{\pm}$-structures, in terms of structured versions of higher dagger categories. This recovers all previously known results, including the description of oriented topological defects in 2-dimensional quantum field theories by pivotal bicategories. Assuming the stratified cobordism hypothesis, we prove our proposal for topological defects with stable tangential structures that admit a direct sum in fully extended topological quantum field theories.
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On the Physics of Higher Condensation Defects
Topological defects from higher gauging are shown, via explicit Lagrangian computations, to satisfy the Karoubi completeness condition of Johnson-Freyd's higher fusion categories, and this is identified with splitting into gauging interfaces.