Chatzistavrakidis, Athanasios; Karagiannis, Georgios; Ranjbar, Arash
(2021)
Duality and Higher Buscher Rules in p ‐Form Gauge Theory and Linearized Gravity.
Fortschritte der Physik, 69
(3).
ISSN 0015-8208
Abstract
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.
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