Recent years have seen a renewed interest in using ‘edge modes’ to extend the pre-symplectic structure of gauge theory on manifolds with boundaries. Here we further the investigation undertaken in [1] by using the formalism of homotopy pullback and Deligne- Beilinson cohomology to describe an electromagnetic (EM) duality on the boundary of M = B³ × ℝ. Upon breaking a generalized global symmetry, the duality is implemented by a BF-like topological boundary term. We then introduce Wilson line singularities on ∂M and show that these induce the existence of dual edge modes, which we identify as connections over a (−1)-gerbe. We derive the pre-symplectic structure that yields the central charge in [1] and show that the central charge is related to a non-trivial class of the (−1)-gerbe.

近年来，人们对使用“边缘模式”扩展具有边界流形上的规范理论的前辛结构产生了新的兴趣。在这里，我们通过使用同伦回调和 Deligne-Beilinson 上同调的形式来进一步研究 [1] 中进行的研究，以描述M = B ³ × ℝ边界上的电磁 (EM) 对偶性。在打破广义全局对称性后，二元性由类似 BF 的拓扑边界项实现。然后我们在∂M上引入威尔逊线奇点，并表明这些会导致双边缘模式的存在，我们将其识别为 a ( -1)-gerbe。我们推导出预辛结构的产率在[1]，并显示该中央充电涉及一种非平凡类的中央电荷（- 1）-gerbe。