Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs

A bstract We present a Sugawara-type construction for boundary charges in 4d BF theory and general family of related TQFTs. Starting from the underlying current Lie algebra symmetries, this gives rise to well-defined quadratic forming an vector fields. In case 3d (i.e. gravity), it was shown [1] that leads two-dimensional diffeomorphism which satisfy certain modular duality. Here we show adapting first requires split gauge algebra. Surprisingly, space generators can then be once again two-dimensional. tangential fields, canonically endows with diff( S 2 ) × or ⋉ vect( ab symmetries depending on The prospect is understand how reduced gravitational symmetry by imposing Plebański simplicity constraints.