Deforming ${\rm AdS}_3\times S^3\times T^4$ in Type IIB Supergravity

We discuss some new results on the construction of supersymmetric solutions of Type IIB supergravity of the form ${\rm WAdS}_3\times{\rm WS}^3\times T^4$, ${\rm WAdS}_3$ and ${\rm WS}^3$ denoting \emph{warped} anti-de Sitter spacetime and sphere, respectively. The distinctive feature of these backgrounds is that, in spite of them being supersymmetric, the warpings of the two factors are described by independent parameters. We illustrate how some of these geometries, characterised by a lightlike warping of the anti-de Sitter factor, arise in the near-horizon limit of a regular, asymptotically locally flat configuration of D-branes and fluxes. Central to the construction of the latter solutions is the use of two independent TsT transformations. We also give a new class of supersymmetric solutions of the general form ${\rm WAdS}_3\times{\rm WS}^3\times T^4$, which has not been published yet. They feature warpings of the anti-de Sitter factor of the lightlike, spacelike and timelike types. We discuss their properties.