Interpolating solution from AdS${}_5$ to hyperscaling violating Lifshitz space-time

Abstract

We construct two interpolating solutions in type II string theory which interpolate between an AdS${}_5$ in the UV and a hyperscaling violating three (spatial) dimensional Lifshitz space-time in the IR. The first solution is non-supersymmetric and is obtained from a known intersecting non-supersymmetric D3-brane with 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 non-constant in general and the metric is three (spatial) dimensional hyperscaling violating Lifshitz 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. 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 AdS${}_5$, whereas in the IR, it gives a three dimensional hyperscaling violating Lifshitz with $z=3$ and $\theta =2=d-1$.

18 pages, no figures; v2: minor changes, references added; v3: several clarifications and references added

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• Thermodynamics of Rotating Kaluza-Klein Black Holes in Gravity's Rainbow
• Thermodynamics of BTZ Black Holes in Gravity's Rainbow
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• Several integrals of quaternionic field on hyperbolic matrix space
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• Crystalline geometries from fermionic vortex lattice with hyperscaling violation
• Non-susy D3 brane and an interpolating solution between AdS${}_5$ black hole, AdS${}_5$ soliton and a `soft-wall' gravity solution