Supersymmetric Warped Solutions from Type IIB Orientifold Reduction

Abstract

We construct a family of supersymmetric solutions in Type IIB supergravity of the form ${\mathrm{WAdS}}_3\times {\mathrm{WS}}^3\times T^4$, where ${\mathrm{WAdS}}_3$ and $\mathrm{W}{\mathrm{S}}^3$ 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 ${\mathrm{WAdS}}_3\times {\mathrm{WS}}^3\times T^4$ with lightlike warped AdS${}_3$ and ${\mathrm{WAdS}}_3\times {\mathrm{S}}^3\times T^4$ in which the warping of AdS${}_3$ is generic. Moreover, we also construct solutions in the form of a warped product ${\mathrm{LM}}_{\hat{I}\P ,\ddot{I}‰}^3{\times }_{\mathrm{w}}{\mathrm{S}}^3\times T^4$ of a 2-parameter deformation ${\mathrm{LM}}_{\hat{I}\P ,\ddot{I}‰}^3$ of ${\mathrm{AdS}}_3$ and a three-sphere. We discuss the relation of these backgrounds to known solutions.

22 pages, latex source. Typos corrected, figure 2 corrected