We construct a family of supersymmetric solutions in Type IIB supergravity of
the form ${\rm WAdS}_3\times {\rm WS}^3\times T^4$, where ${\rm WAdS}_3$ and
${\rm WS^3}$ denote a warped anti-de Sitter spacetime and a warped 3-sphere,
respectively, while $T^4$ denotes an internal 4-torus. These backgrounds are
constructed by uplifting corresponding solutions in the $D=6$,
$\mathcal{N}=(1,1)$ ungauged supergravity resulting from the compactification
of Type IIB supergravity on a $T^4/\mathbb{Z}_2$-orientifold. More
specifically, the supersymmetric solutions are ${\rm WAdS}_3\times {\rm
WS}^3\times T^4$ with lightlike warped AdS$_3$ and ${\rm WAdS}_3\times {\rm
S}^3\times T^4$ in which the warping of AdS$_3$ is generic. Moreover, we also
construct solutions in the form of a warped product
$\mathrm{LM}^3_{\zeta,\omega}\times_{{\rm w}} \mathrm{S}^3\times T^4$ of a
2-parameter deformation $\mathrm{LM}^3_{\zeta,\omega}$ de ${\rm AdS}_3$ and a
three-sphere. We discuss the relation of these backgrounds to known solutions.

Cet article explore les excursions dans le temps et leurs implications.

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