Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.
D-branes and K-theory in 2D topological field theory
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abstract
This expository paper describes sewing conditions in two-dimensional open/closed topological field theory. We include a description of the G-equivariant case, where G is a finite group. We determine the category of boundary conditions in the case that the closed string algebra is semisimple. In this case we find that sewing constraints -- the most primitive form of worldsheet locality -- already imply that D-branes are (G-twisted) vector bundles on spacetime. We comment on extensions to cochain-valued theories and various applications. Finally, we give uniform proofs of all relevant sewing theorems using Morse theory.
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Open Virasoro TQFT computes 3d gravity path integrals on compact regions using threshold-dependent boundary conditions and yields an open-closed duality relating Conformal Turaev-Viro theory to the diagonal sector of two Virasoro TQFT copies.
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
Surveys nearly Frobenius algebras, generalizations of Frobenius algebras without traces, along with basic results and applications in geometry, topology, and representation theory.
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What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.