Consistent truncations to 3-dimensional supergravity

We show how to construct consistent truncations of 10-/11-dimensional supergravity 3-dimensional gauged supergravity, preserving various amounts supersymmetry. show, that as in higher dimensions, can be defined terms generalised $G$-structures Exceptional Field Theory, with $G \subset E_{8(8)}$ for the case. Differently from Lie derivative $E_{8(8)}$ Theory requires a set "covariantly constrained" fields well-defined, and we these constructed $G$-structure itself. prove several general features truncations, allowing us rule out higher-dimensional origin many supergravities. In particular, compact part gauge group at most $\mathrm{SO}(9)$ there are no on 7-or 8-dimensional product spheres such full isometry is gauged. Moreover, classify which matter-coupled ${\cal N} \geq 4$ supergravities arise truncations. Finally, give examples three dimensions. These include IIA IIB $S^7$ leading two different N}=16$ supergravites, well more IIA/IIB $H^{p,7-p}$. also compactifications $S^5$ fibred over Riemann surface. result N}=4$ scalar manifold M} = \frac{\mathrm{SO}(6,4)}{\mathrm{SO}(6) \times \mathrm{SO}(4)} \frac{\mathrm{SU}(2,1)}{\mathrm{S}(\mathrm{U}(2)\times\mathrm{U}(1))}$ $\mathrm{ISO}(3)\times\mathrm{U}(1)^4$ gauging hyperboloidal surfaces contain N}=(2,2)$ AdS$_3$ vacua.