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

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