Abstract
IIB supergravity is reformulated with a manifest local USp(8) invariance that makes the embedding of five-dimensional maximal supergravities transparent. In this formulation the ten-dimensional theory exhibits all the 27 one-form fields and 22 of the 27 two-form fields that are required by the vector-tensor hierarchy of the five-dimensional theory. The missing 5 two-form fields must transform in the same representation as a descendant of the ten-dimensional `dual graviton'. The invariant E6(6) symmetric tensor that appears in the vector-tensor hierarchy is reproduced. Generalized vielbeine are derived from the supersymmetry transformations of the vector fields, as well as consistent expressions for the USp(8) covariant fermion fields. Implications are discussed for the consistency of the truncation of IIB supergravity compactified on the five-sphere to maximal gauged supergravity in five space-time dimensions with an SO(6) gauge group.
Highlights
Fields that still depend on all eleven space-time coordinates
IIB supergravity is reformulated with a manifest local USp(8) invariance that makes the embedding of five-dimensional maximal supergravities transparent
Implications are discussed for the consistency of the truncation of IIB supergravity compactified on the five-sphere to maximal gauged supergravity in five space-time dimensions with an SO(6) gauge group
Summary
We summarize the relevant results for IIB supergravity in ten space-time dimensions [29,30,31]. In what follows we use the convenient notation φα ≡ ηαβ(φβ)∗, with ηαβ = diag(+1, −1), so that the above constraint reads φαφα = 1. In this convention the vector fields take the following form, QM = − iφα ∂M φα , PM = εαβ φα DM φβ , PM = − εαβ φα DM φβ ,. The tensor fields are subject to rigid SU(1, 1) transformations, just as the scalar fields φα, and to tensor gauge transformations. The latter read δAαMN = 2 ∂[M ΞαN]. In addition there is a constraint on the 5-index field strength which involves the dual field strength,
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