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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.

Duality and Higher Buscher Rules in p ‐Form Gauge Theory and Linearized Gravity