Consistent $S^3$ reductions of six-dimensional supergravity

We work out the consistent AdS${}_3\times S^3$ truncations of the bosonic sectors of both the six-dimensional $\mathcal{N}=(1,1)$ and $\mathcal{N}=(2,0)$ supergravity theories. They result in inequivalent three-dimensional half-maximal $\mathrm{S}\mathrm{O}(4)$ gauged supergravities describing 32 propagating bosonic degrees of freedom apart from the non-propagating supergravity multiplet. We present the full non-linear Kaluza-Klein reduction formulas and illustrate them by explicitly uplifting a number of AdS${}_3$ vacua.