论文标题
在4D BF理论和相关TQFT中，二型二型作为二次电荷
Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs
论文作者
论文摘要
我们提出了4D BF理论和一般性TQFT家族中边界电荷的Sugawara型结构。从边界对称性的基本电流代数开始，这产生了构成矢量场代数的明确定义的二次电荷。在3D BF理论（即3D重力）的情况下，它在[PRD 106（2022），ARXIV：2012.05263 [HEP-TH]中显示，这种构建导致了二维差异性型电荷家族，从而满足了某个模块化双重性。在这里，我们表明，将这种结构适应为4D BF理论首先需要将基本量规代数分开。令人惊讶的是，可以证明明确定义的二次发电机的空间再次是二维。在切向量矢量字段的情况下，这在规范上赋予4D BF理论，具有$ \ MATHRM {diff}（s^2）（s^2）\ times \ times \ Mathrm {diff}（s^2）$或$ \ mathrm {diff}（diff}（s^2）边界对称性取决于量规代数。然后，前景是了解如何通过施加plebański简单性约束来将其简化为引力对称代数。
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 $\mathrm{diff}(S^2)\times\mathrm{diff}(S^2)$ or $\mathrm{diff}(S^2)\ltimes\mathrm{vect}(S^2)_\mathrm{ab}$ 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 Plebański simplicity constraints.
