Symplectic Deformations of Gauged Maximal Supergravity

TL;DR

The paper formalizes a general framework for symplectic deformations of gauged maximal supergravity in four dimensions, defining the deformation space 𝔖 via the normalizer of the gauge group within the symplectic group and quotienting by physically redundant field redefinitions. Using the embedding tensor formalism, the authors show how inequivalent gaugings arise from different symplectic embeddings of the same gauge algebra, and they derive both a full and a reduced deformation space 𝔖 and 𝔖_red that separate deformations affecting the equations of motion from those equivalent up to non-dynamical frame changes. They perform a detailed group-theoretical analysis for SO(8), and extend the analysis to gaugings contained in SL(8,R) and SU*(8), including CSS and CSO-type settings; key findings include the ω-deformation of SO(8) together with a gauge-invariant θ-term, as well as discrete dyonic deformations in ISO(p,7-p) and related gaugings. The results illuminate how continuous deformation parameters can persist in gauged supergravities and potentially influence quantum corrections and the landscape of AdS and Minkowski vacua, with implications for string theory embeddings and dual field theories.

Abstract

We identify the space of symplectic deformations of maximal gauged supergravity theories. Coordinates of such space parametrize inequivalent supergravity models with the same gauge group. We apply our procedure to the SO(8) gauging, extending recent analyses. We also study other interesting cases, including Cremmer-Scherk-Schwarz models and gaugings of groups contained in SL(8,R) and in SU*(8).