Consistent SO(6) reduction of type IIB supergravity on S

Abstract

Type IIB supergravity can be consistently truncated to the metric and the self-dual 5-form. We obtain the complete non-linear Kaluza-Klein S 5 reduction Ansatz for this theory, giving rise to gravity coupled to the fifteen Yang-Mills gauge fields of SO(6) and the twenty scalars of the coset SL(6, IR)/SO(6). This provides a consistent embedding of this subsector of N = 8, D = 5 gauged supergravity in type IIB in D = 10. We demonstrate that the self-duality of the 5-form plays a crucial role in the consistency of the reduction. We also discuss certain necessary conditions for a theory of gravity and an antisymmetric tensor in an arbitrary dimension D to admit a consistent sphere reduction, keeping all the massless fields. We find that it is only possible for D = 11, with a 4-form field, and D = 10, with a 5-form. Furthermore, in D = 11 the full bosonic structure of eleven-dimensional supergravity is required, while in D = 10 the 5-form must be self-dual. It is remarkable that just from the consistency requirement alone one would discover D = 11 and type IIB supergravities, and that D = 11 is an upper bound on the dimension.

Spheres, Generalised Parallelisability and Consistent Truncations

“…As we will see, for the cases of interest, this exactly agrees with the standard scalar field ansatz for sphere consistent truncations [30,40,10,35,11,34]. 2 Note that the factor of 1 2 comes from the normalisation (2.29).…”

“…where η is the usual 11) and G is the generalised metric (2.24) (with ∆ = 0). Under the generalised Lie derivative the algebra reads…”

“…The metric and five-form flux subsector was shown to be consistent in [11,34], but otherwise there is no complete derivation of consistency. In the following we will show that generalised parallelisable structure (3.39) reproduces the correct gauge structure and matches the known scalar ansatz for g mn and A m 1 ...m 4 .…”

Attractors, black objects and holographic RG flows in 5d maximal gauged supergravities

“…The maximal compact gauge group of N = 8 is SO (6) and has a clear M-theory origin as a compactification on S 5 [20]. More generally there are versions of N = 8 with a gauge group SO(p, 6 − p) for any integer p [3], as well as other smaller gauge groups that can be accomodated in maximal supergravity by the embedding tensor formalism [21].…”

Consistent Kaluza-Klein sphere reductions

“…In addition to keeping the corresponding Yang-Mills fields A ij (1) and scalars T ij , the consistency of the S 4 reduction requires also keeping the five 3-forms A i (3) of the seven-dimensional theory, whilst the S 7 reduction instead requires also keeping the 35 pseudoscalars φ [ijkℓ] + (self-dual in the SO(8) indices). These additional fields are needed in the reductions because the Yang-Mills fields act as sources for them [18]. In fact we can summarise the situation in all three of these examples of the S 4 , S 7 and S 5 reductions as follows.…”