Dualities play a central role in both quantum field theories and condensed matter systems. Recently, a web of dualities has been discovered in 2+1 dimensions. Here, we propose in particular a generalization of the Son's fermion-fermion duality to 3+1 dimensions. We show that the action of charged Dirac fermions coupled to an external electromagnetic field is dual to an action of neutral fermions minimally coupled to an emergent vector gauge field. This dual action contains also a further tensor (Kalb-Ramond) gauge field coupled to the emergent and electromagnetic vector potentials. We firstly demonstrate the duality in the massive case. We then show the duality in the case of massless fermions starting from a lattice model and employing the slave-rotor approach already used in the 2+1-dimensional duality [Burkov, Phys. Rev. B 99, 035124 (2019)]. We finally apply this result to 3D Dirac semimetals in the low-energy regime. Besides the implications in topological phases of matter, our results shed light on the possible existence of a novel web of dualities in 3+1-dimensional (non-supersymmetric) quantum field theories.

中文翻译：

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3+1 维中的费米子-费米子对偶性

二元性在量子场论和凝聚态系统中都发挥着核心作用。最近，在 2+1 维中发现了一个二元网络。在这里，我们特别建议将子的费米子-费米子对偶性推广到 3+1 维。我们表明，带电狄拉克费米子与外部电磁场耦合的作用与中性费米子与涌现矢量规范场最小耦合的作用是双重的。这种双重作用还包含一个进一步的张量（Kalb-Ramond）规范场，它耦合到涌现和电磁矢量势。我们首先证明了大规模情况下的二重性。然后，我们展示了无质量费米子情况下的对偶性，从一个晶格模型开始，并采用已经在 2+1 维对偶中使用的从动转子方法 [Burkov, Phys. 修订版 B 99，035124 (2019)]。我们最终将这个结果应用于低能区的 3D Dirac 半金属。除了对物质拓扑相的影响之外，我们的结果还阐明了 3+1 维（非超对称）量子场论中可能存在一种新的二元性网络。