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

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.

Duality, Generalized Global Symmetries and Jet Space Isometries

“…Let us now move on to 4D nonlinear Abelian gauge theories admitting SO(2) electricmagnetic duality rotations and present a systematic procedure for their off-shell dualization. This essentially extends the results presented in [20] for linear theories and it reflects the general spirit, e.g., [16,[37][38][39][40][41]. The dynamical field is now a 1-form gauge field A with Abelian gauge transformation δA = dΛ ,…”

“…This set of rules holds true for all corresponding sigma models of differential 2p-form fields in selfdual dimensions, e.g., 2-forms in 6 dimensions, with a kinetic term and a generalized theta term that corresponds to the antisymmetric coupling B ij . For more details see [12,20].…”

“…One final comment is that this procedure can take into account the inversion of the dimensionless electromagnetic coupling e. Had the first term in (97) been 1 e 2 k |g| d 4 σ, we would have found that the first term in (98) becomes e 2 k |g| d 4 σ. This analysis is rather easily extended to the case of the electromagnetic θ-term; a complete discussion is found in [20], see also [42] for a path integral derivation.…”

“…This sigma model philosophy is well motivated by the fact that the photon appears as a Nambu-Goldstone boson from this point of view. Remarkably, this also gives rise to a set of Buscher-like duality rules [20], which acquire a suggestive form when written in terms of the complexified coupling. Apart from discussing all these features, in this paper we make a first attempt to interpret generalized global symmetries as generalized isometries of the configuration space, at least in Abelian 1-form theories.…”

Topological field theories induced by twisted R-Poisson structure in any dimension

“…One should note that such a term also exists in the Abelian theory, with certain physical applications such as in the effective field theory of topological insulators [5] and topological superconductors [6]. The deformation (5.47) is of this nature, at least if one thinks of Y i as an exact (p−1)-form, and it corresponds to a generalised theta term in presence of multiple fields, and therefore it is not surprising that it comes with a symmetric background field (see also [40] for further explanations on this point.) However, in the spirit of the present paper we would like to think of this term as accompanying the theory given by the action functional (5.44), and also of Y i as a gauge field rather than a field strength.…”