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arXiv · 2411.13012

A toy model for $p$-form gauge symmetry

Yi Yan·Zhao-Long Wang
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Abstract

The abelian $(p+1)$-form gauge field is inherently coupled to the $p$-brane worldvolume. After quantization, the corresponding $p$-form gauge transformation is associated with the local phase ambiguity of the $p$-brane wave functional. In essence, the $p$-form gauge symmetry can be realized as a special construction of the generic 0-form gauge symmetry in the functional space of $p$-brane configurations. The non-abelian generalization is straightforward in the functional space language. To simplify the analysis, we further introduce a toy model where the infinite dimensional functional space of $p$-brane configurations is replaced by a finite dimensional matrix space. After taking the symmetric trace in the matrix model, the original discussions of the $p$-form gauge symmetry can be inherited by the toy model.

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Yi Yan, Zhao-Long Wang. 2024-11-20. A toy model for $p$-form gauge symmetry. https://doi.org/10.1088/1572-9494%2Fadcaa7

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