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August 27, 2023 to September 8, 2023
SRS
Europe/Zurich timezone

Kevin Walker: Categorified idempotent completion, topological symmetries of QFTs, and generalized Kramers-Wannier duality

Aug 31, 2023, 11:15 AM
1h
SRS

SRS

Hotel Les Sources Chemin du Vernex 9 1865 Les Diablerets Switzerland

Description

Any (n-pivotal) n-category C can be embedded in a Morita-equivalent completion C^#. Because of the Morita equivalence, any module/action of C automatically leads to one of the larger category C^#. In particular, discrete k-form symmetries of d-dimensional QFTs correspond to actions of C(G, d+1, k+1) = \pi_{\le d+1}(B^{k+1}(G)), and therefore give rise to actions of the completed (d+1)-category C(G, d+1, k+1)^#. While C(G, d+1, k+1) is built out of invertible morphisms, C(G, d+1, k+1)^# typically contains many non-invertible morphisms leading to non-invertible symmetries of the original QFT. I’ll also discuss how completed n-categories can be used to construct many new examples of Kramers-Wannier-type dualities. This is joint work with Fiona Burnell.

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