Algebra of symmetry in BF-like models in 3d and 4d

In this talk, I will discuss the construction of the boundary symmetry algebra for BF-like theories in 3D and 4D. In the 3D case, the theory corresponds to (an extension of) 3D gravity allowing for a source of curvature and torsion. I will show how the study of the current algebra and its associated Sugawara construction allows for two notions of quadratic charges (the usual diffeomorphism and its "dual") independently of boundary conditions. I will discuss their resulting algebra and its relation with the usual construction of the asymptotic boundary algebra. In the 4D case, a similar yet fundamentally different construction is possible, similarly resulting in multiple quadratic charges. I will discuss their constructions and their possible relations to 4D gravity.