Abstract
Four-dimensional ${\cal N}=2$ gauged STU supergravity is a consistent truncation of the standard ${\cal N}=8$ 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 ${\cal N}=2$ 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 $\omega$-deformed ${\cal N}=8$ gauged $SO(8)$ supergravities, thereby obtaining a family of $\omega$-deformed STU gauged supergravities. Unlike in some other truncations of the deformed ${\cal N}=8$ supergravity that have been considered, here the scalar potential of the deformed STU theory is independent of the $\omega$ 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 $\omega$-deformed supergravities, and present some examples of black hole solutions.
Highlights
Of N = 4 gauged SO(4) supergravity.1 In both cases, with the embedding we consider, we find that the scalar potential of the truncated theory no longer carries any dependence on the deformation parameter of the larger N = 8 theory, even though the N = 8 potential does, depend upon ω
For consistency, four of the six scalar fields are set to zero, leaving just a single dilaton/axion pair. In this truncation it turns out that the ω dependence in the scalar couplings of the kinetic terms for the remaining two gauge fields can be removed merely by using a shift symmetry of the axionic scalar, with no need to perform any dualisation of the gauge fields, and so the entire theory becomes independent of the ω parameter
For the embedding we adopt, we find that the same thing happens; namely, that the scalar potential is independent of ω and that the ω-dependence in the scalar couplings to the gauge-field kinetic terms can be eliminated by means of a shift symmetry transformation of the axionic scalar
Summary
The standard gauged STU supergravity theory can be obtained as a consistent truncation of standard N = 8 gauged SO(8) supergravity In this embedding, the SO(8) gauge fields are truncated to retain only those in the U(1) Cartan subalgebra of SO(8). The complete embedding of the bosonic sector of the gauged STU model, including the axions, was given in [15]. This was achieved by giving an explicit form for the 56-bein. The scalar potential V is defined in the standard way in N = 8 gauged SO(8) supergravity, except that with the ω deformation the definition of the T tensor is modified. The four gauge fields of the deformed STU model are taken to be in the U(1) Cartan subalgebra of the SO(8)
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