论文标题
二元性和较高的Buscher规则在P形仪表理论和线性重力中
Duality and higher Buscher rules in p-form gauge theory and linearized gravity
论文作者
论文摘要
我们对包含多个标量，$ p $ - 形式仪表字段，线性化的重力或$（p，1）$混合对称性张量的理论的耦合对二元性进行了深入分析。在与t偶尔下的字符串背景字段的派生类似的推理之后，我们表明，所有上述多场理论的耦合都根据两组二元性规则之一转换。这些集合包括普通的Buscher规则及其更高的对应物；这是时空维度中多场理论的通用特征，在时空维度中，场强度及其双重程度相同。我们的分析考虑了拓扑术语和广义$ b $ fields，其双重性行为经过仔细跟踪。对于4D中的1形或重力，这将减少为电气/磁双重性下的复杂耦合或广义度量的反转。此外，我们在存在$θ$ - 期的情况下写下了线性化重力的动作，从中我们从中获得了先前建议的壳双重性和双重性关系。这也为引力双重关系中theta的起源提供了解释，作为线性重力作用的特定附加区域。
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.
