Consistent truncations to 3-dimensional supergravity

Abstract

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 ⊂ E 8(8) for the 3-dimensional case. Differently from higher dimensions, the generalised Lie derivative of E 8(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 N $$ \mathcal{N} $$ ≥ 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 S 7 leading to two different N $$ \mathcal{N} $$ = 16 gauged supergravites, as well as more general IIA/IIB truncations on H p,7−p . We also show how to construct consistent truncations of IIB supergravity on S 5 fibred over a Riemann surface. These result in 3-dimensional N $$ \mathcal{N} $$ = 4 gauged supergravities with scalar manifold M = SO 6 4 SO 6 × SO 4 × SU 2 1 S U 1 × U 2 $$ \mathcal{M}=\frac{\mathrm{S}\mathrm{O}\left(6,4\right)}{\mathrm{S}\mathrm{O}(6)\times \mathrm{SO}(4)}\times \frac{\mathrm{S}\mathrm{U}\left(2,1\right)}{\mathrm{S}\left(\mathrm{U}(1)\times \mathrm{U}(2)\right)} $$ with a ISO(3) × U(1)4 gauging and for hyperboloidal Riemann surfaces contain N $$ \mathcal{N} $$ = (2, 2) AdS3 vacua.

Keywords

• AdS-CFT Correspondence
• Flux Compactifications
• Supergravity Models
• Superstring Vacua