We describe a construction of generalized Maxwell theories – higher analogues of abelian gauge theories – in the factorization algebra formalism of Costello and Gwilliam, allowing for analysis of the structure of local observables. We describe the phenomenon of abelian duality for local observables in these theories as a form of Fourier duality, relating observables in theories with dual abelian gauge groups and inverted coupling constants in a way compatible with the local structure. We give a description of expectation values in this theory and prove that duality preserves expectation values. Duality is shown to, for instance, interchange higher analogues of Wilson and ’t Hooft operators.

中文翻译：

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广义麦克斯韦理论的阿贝尔对偶性

我们在 Costello 和 Gwilliam 的分解代数形式主义中描述了广义麦克斯韦理论的构建——阿贝尔规范理论的更高类似物——允许分析局部可观察量的结构。我们将这些理论中局部可观测量的阿贝尔对偶现象描述为傅立叶对偶的一种形式，将理论中的可观测量与对偶阿贝尔规范群和反耦合常数以与局部结构兼容的方式联系起来。我们对该理论中的期望值进行了描述，并证明了对偶性保留了期望值。例如，二元性被证明可以互换 Wilson 和 't Hooft 算子的更高类似物。