Electromagnetic duality and central charge
Electromagnetic duality and central charge
复制标题
电磁二象性和中心电荷
DOI：
10.1103/physrevd.98.116008
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发表时间：
2018
影响因子：
5
通讯作者：
D. Pranzetti
中科院分区：
文献类型：
--
作者：
L. Freidel;D. Pranzetti
我们通过引入边缘模及其共轭动量扩展了麦克斯韦理论的相空间，从而提供了边界处电磁对偶性的完整实现。我们展示了如何这样的扩展，这是从一个边界行动，是必要的，以便有明确的规范生成的边界磁对称性。这样，电和磁软模都被编码在边界规范场及其共轭对偶中。电磁对偶性的这种实现具有惊人的后果。特别地，我们首先展示了电荷量子化是如何从边界对偶势的$U（1）$-丛的拓扑性质直接得出的。此外，有一个明确定义的规范作用的电和磁对称发电机的相空间，我们可以计算它们的代数和揭示它们之间的中心电荷的存在。最后，我们总结了这些结果在量子理论中的可能含义。
We provide a full realization of the electromagnetic duality at the boundary by extending the phase space of Maxwell's theory through the introduction of edge modes and their conjugate momenta. We show how such extension, which follows from a boundary action, is necessary in order to have well defined canonical generators of the boundary magnetic symmetries. In this way, both electric and magnetic soft modes are encoded in a boundary gauge field and its conjugate dual. This implementation of the electromagnetic duality has striking consequences. In particular, we show first how the electric charge quantization follows straightforwardly from the topological properties of the $U(1)$-bundle of the boundary dual potential. Moreover, having a well defined canonical action of the electric and magnetic symmetry generators on the phase space, we can compute their algebra and reveal the presence of a central charge between them. We conclude with possible implications of these results in the quantum theory.