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• W4309757951 abstract "The gauge symmetry and shift/translational symmetry of a 3D BF action, which are associated to a pair of dual Lie algebras, can be combined to form the Drinfel'd double. This combined symmetry is the gauge symmetry of the Chern-Simons action which is equivalent to the BF action, up to some boundary term. We show that something similar happens in 4D when considering a 2-BF action (aka BFCG action), whose symmetries are specified in terms of a pair of dual strict Lie 2-algebras (ie. crossed-modules). Combining these symmetries gives rise to a 2-Drinfel'd double which becomes the gauge symmetry structure of a 4D BF theory, up to a boundary term. Concretely, we show how using 2-gauge transformations based on dual crossed-modules, the notion of 2-Drinfel'd double defined in Ref. arXiv:1109.1344 appears. We also discuss how, similarly to the Lie algebra case, the symmetric contribution of the $r$-matrix of the 2-Drinfel'd double can be interpreted as a quadratic 2-Casimir, which allows to recover the notion of duality." @default.
• W4309757951 created "2022-11-29" @default.
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• W4309757951 date "2022-11-21" @default.
• W4309757951 modified "2023-10-16" @default.
• W4309757951 title "Categorified Drinfel’d double and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>B</mml:mi><mml:mi>F</mml:mi></mml:math> theory: 2-groups in 4D" @default.
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• W4309757951 doi "https://doi.org/10.1103/physrevd.106.105017" @default.
• W4309757951 hasPublicationYear "2022" @default.
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