We construct two interpolating solutions in type II string theory which interpolate between ${\mathrm{AdS}}_5$ in the UV and a hyperscaling-violating three (spatial)-dimensional Lifshitz spacetime in the IR. The first solution is nonsupersymmetric and is obtained from a known intersecting nonsupersymmetric D3-brane with a chargeless D0-brane solution of type IIB string theory, by restricting some parameters characterizing the solution and going to a new coordinate. In the IR the dilaton is nonconstant in general and the metric is three (spatial)-dimensional hyperscaling-violating Lifshitz spacetime with dynamical critical exponent $z=(3+3\gamma )/(3-\gamma )$ and hyperscaling-violation exponent $\theta =12/(3-\gamma )$, where $\gamma$ is a real parameter and can take continuous values from $-1$ to $+1$. At the two extreme values, i.e., for $\gamma =\pm 1$, the dilaton is constant. On physical grounds it is found that $\gamma$ must be restricted to lie in the range $-1\le \gamma \le 0$. The second solution is supersymmetric and is obtained from the known F-D2 bound-state solution of type IIA string theory by zooming into a particular region of space. In the UV, the proper description is given in a $T$-dual frame which is ${\mathrm{AdS}}_5$, whereas in the IR, it gives a three-dimensional hyperscaling-violating Lifshitz spacetime with $z=3$ and $\theta =2=d-1$.

• Received 7 November 2014

DOI:https://doi.org/10.1103/PhysRevD.91.026005