Consistent truncations to 3-dimensional supergravity

Abstract

We show how to construct consistent truncations of 10-/11-dimensional supergravity to 3-dimensional gauged supergravity, preserving various amounts of supersymmetry. We show, that as in higher dimensions, consistent truncations can be defined in terms of generalised G-structures in Exceptional Field Theory, with G ⊂ E8(8) for the 3-dimensional case. Differently from higher dimensions, the generalised Lie derivative of E8(8) Exceptional Field Theory requires a set of “covariantly constrained” fields to be well-defined, and we show how these can be constructed from the G-structure itself. We prove several general features of consistent truncations, allowing us to rule out a higher-dimensional origin of many 3-dimensional gauged supergravities. In particular, we show that the compact part of the gauge group can be at most SO(9) and that there are no consistent truncations on a 7-or 8-dimensional product of spheres such that the full isometry group of the spheres is gauged. Moreover, we classify which matter-coupled mathcal{N} ≥ 4 gauged supergravities can arise from consistent truncations. Finally, we give several examples of consistent truncations to three dimensions. These include the truncations of IIA and IIB supergravity on S7 leading to two different mathcal{N} = 16 gauged supergravites, as well as more general IIA/IIB truncations on Hp,7−p. We also show how to construct consistent truncations of IIB supergravity on S5 fibred over a Riemann surface. These result in 3-dimensional mathcal{N} = 4 gauged supergravities with scalar manifold mathcal{M}=frac{mathrm{S}mathrm{O}left(6,4right)}{mathrm{S}mathrm{O}(6)times mathrm{SO}(4)}times frac{mathrm{S}mathrm{U}left(2,1right)}{mathrm{S}left(mathrm{U}(1)times mathrm{U}(2)right)} with a ISO(3) × U(1)4 gauging and for hyperboloidal Riemann surfaces contain mathcal{N} = (2, 2) AdS3 vacua.