In this work, we revisit the duality between a self-dual non-gauge invariant theory and a topological massive theory in $3+1$ dimensions. The self-dual Lagrangian is composed by a vector field and an antisymmetric field tensor whereas the topological massive Lagrangian is build using a $B \wedge F$ term. Though the Lagrangians are quite different, they yield to equations of motion that are connected by a simple dual mapping among the fields. We discuss this duality by analyzing the degrees of freedom in both theories and comparing their propagating modes at the classical level. Moreover, we employ the master action method to obtain a fundamental Lagrangian that interpolates between these two theories and makes evident the role of the topological $B \wedge F$ term in the duality relation. By coupling these theories with matter fields, we show that the duality holds provided a Thirring-like term is included. In addition, we use the master action in order to probe the duality upon the quantized fields. We carried out a functional integration of the fields and compared the resulting effective Lagrangians.

中文翻译：

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自对偶和拓扑质量 B∧F 模型在 3+1 维耦合到物质之间的对偶等价

在这项工作中，我们重新审视了自对偶非规范不变理论和 $3+1$ 维度的拓扑大规模理论之间的对偶性。自对偶拉格朗日量由向量场和反对称场张量组成，而拓扑质量拉格朗日量是使用 $B \wedge F$ 项构建的。尽管拉格朗日量是完全不同的，但它们屈服于通过场之间的简单对偶映射连接的运动方程。我们通过分析两种理论的自由度并比较它们在经典水平上的传播模式来讨论这种二元性。此外，我们采用主作用方法来获得在这两种理论之间进行插值的基本拉格朗日量，并表明拓扑 $B\wedge F$ 项在对偶关系中的作用。通过将这些理论与物质场相结合，我们表明，如果包含类似 Thirring 的术语，则二元性成立。此外，我们使用主动作来探测量化场的二元性。我们对这些领域进行了功能整合，并比较了由此产生的有效拉格朗日函数。