We perform an in‐depth analysis of the transformation rules under duality for couplings of theories containing multiple scalars, p‐form gauge fields, linearized gravitons or (p, 1) mixed symmetry tensors. Following a similar reasoning to the derivation of the Buscher rules for string background fields under T‐duality, we show that the couplings for all classes of aforementioned multi‐field theories transform according to one of two sets of duality rules. These sets comprise the ordinary Buscher rules and their higher counterpart; this is a generic feature of multi‐field theories in spacetime dimensions where the field strength and its dual are of the same degree. Our analysis takes into account topological theta terms and generalized B‐fields, whose behavior under duality is carefully tracked. For a 1‐form or a graviton in 4D, this reduces to the inversion of the complexified coupling or generalized metric under electric/magnetic duality. Moreover, we write down an action for linearized gravity in the presence of θ‐term from which we obtain previously suggested on‐shell duality and double duality relations. This also provides an explanation for the origin of theta in the gravitational duality relations as a specific additional sector of the linearized gravity action.

中文翻译：

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p形规理论和线性重力的对偶性和高级Buscher规则

我们对包含多个标量，p形规范场，线性化引力子或（p，1）混合对称张量的理论在对偶下的转换规则进行了深入分析。遵循与推导T-对偶关系下的字符串背景字段的Buscher规则相似的推理，我们表明，上述多场理论的所有类别的耦合都根据两组对偶规则中的一组进行变换。这些集合包括普通的Buscher规则及其较高的对等规则；这是时空维度上多场理论的普遍特征，其中场强及其对偶具有相同程度。我们的分析考虑了拓扑theta项和广义B场，仔细跟踪其在二元性下的行为。对于1形式或4D引力子，这减少了电磁/电磁对偶下复杂耦合或广义度量的求逆。此外，我们在存在θ项的情况下记下了线性化重力的作用，从中我们获得了先前建议的壳对偶性和双重对偶关系。这也解释了作为线性化重力作用的特定附加部分的引力对偶关系中theta的起源。