An ExFT-based algorithm reduces the uplift problem to a PDE on the base of the internal manifold and classifies the type IIB uplifts of pure SO(4)-gauged N=4 supergravity by two harmonic functions on a Riemann surface.
Gauged maximal supergravities and hierarchies of nonabelian vector-tensor systems
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abstract
We describe generalizations of the manifestly E_{6(6)} covariant formulation of five-dimensional gauged maximal supergravity with regard to the structure of the vector and tensor fields. We indicate how the group-theoretical structures that we discover seem to play a role in gauged supergravities in various space-time dimensions.
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How to uplift non-maximal gauged supergravities
An ExFT-based algorithm reduces the uplift problem to a PDE on the base of the internal manifold and classifies the type IIB uplifts of pure SO(4)-gauged N=4 supergravity by two harmonic functions on a Riemann surface.