On the Physics of Higher Condensation Defects

Abstract: We study the structure of topological defects for finite Abelian symmetries in quantum field theories, and argue on physical grounds that they satisfy the definition of a higher fusion category proposed by Johnson-Freyd. Our primary focus is on the requirement of Karoubi completeness, i.e. the factorization conditions on higher condensation defects. We demonstrate this on a tree of such defects, constructed by successive higher gauging, explicitly using Lagrangian techniques in a concrete four-dimensional example, before turning to more general field theories. Along the way we also comment on the phenomenon where decoupled topological field theories appear as fusion coefficients. We further discuss the categorical role of anomalies, and how they may affect the properties of (higher) condensation defects.