An $\ddot{I}‰$ Deformation of Gauged STU Supergravity

Abstract

Four-dimensional $\mathcal{N}=2$ gauged STU supergravity is a consistent truncation of the standard $\mathcal{N}=8$ gauged $SO(8)$ supergravity in which just the four $U(1)$ gauge fields in the Cartan subgroup of $SO(8)$ are retained. One of these is the graviphoton in the $\mathcal{N}=2$ supergravity multiplet and the other three lie in three vector multiplets. In this paper we carry out the analogous consistent truncation of the newly-discovered family of $\ddot{I}‰$-deformed $\mathcal{N}=8$ gauged $SO(8)$ supergravities, thereby obtaining a family of $\ddot{I}‰$-deformed STU gauged supergravities. Unlike in some other truncations of the deformed $\mathcal{N}=8$ supergravity that have been considered, here the scalar potential of the deformed STU theory is independent of the $\ddot{I}‰$ parameter. However, it enters in the scalar couplings in the gauge-field kinetic terms, and it is non-trivial because of the minimal couplings of the fermion fields to the gauge potentials. We discuss the supersymmetry transformation rules in the $\ddot{I}‰$-deformed supergravities, and present some examples of black hole solutions.

31 pages. Derivation of the range of ωcorrected; discussion of supersymmetry of solutions extended, and a reference added