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- W4308014722 abstract "We present a Sugawara-type construction for boundary charges in 4d BF theory and in a general family of related TQFTs. Starting from the underlying current Lie algebra of boundary symmetries, this gives rise to well-defined quadratic charges forming an algebra of vector fields. In the case of 3d BF theory (i.e. 3d gravity), it was shown in [PRD 106 (2022), arXiv:2012.05263 [hep-th]] that this construction leads to a two-dimensional family of diffeomorphism charges which satisfy a certain modular duality. Here we show that adapting this construction to 4d BF theory first requires to split the underlying gauge algebra. Surprisingly, the space of well-defined quadratic generators can then be shown to be once again two-dimensional. In the case of tangential vector fields, this canonically endows 4d BF theory with a $mathrm{diff}(S^2)timesmathrm{diff}(S^2)$ or $mathrm{diff}(S^2)ltimesmathrm{vect}(S^2)_mathrm{ab}$ algebra of boundary symmetries depending on the gauge algebra. The prospect is to then understand how this can be reduced to a gravitational symmetry algebra by imposing Pleba'nski simplicity constraints." @default.
- W4308014722 created "2022-11-07" @default.
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- W4308014722 date "2022-10-31" @default.
- W4308014722 modified "2023-10-14" @default.
- W4308014722 title "Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs" @default.
- W4308014722 doi "https://doi.org/10.48550/arxiv.2211.00068" @default.
- W4308014722 hasPublicationYear "2022" @default.
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