From AdS to Schrödinger/Lifshitz dual space-times without or with hyperscaling violation

Abstract

It is observed that the (intersecting) branes of M/string theory, which are known to give AdS geometry (directly or upto a conformal transformation) in the near horizon limit, do also lead to Schr\" odinger/Lifshitz dual space-times (without or with hyperscaling violation) upon using appropriate solution generating transformation and dimensional reduction. We show that the dynamical exponents of the Schr\" odinger and the Lifshitz space-times obtained in this way always add upto 2. We illustrate this by several examples, including M2-, M5-branes of M-theory and D$(p+1)$-branes ($p\ne 4$, since in this case the near horizon limit does not give AdS geometry) of string theory as well as many of their intersecting solutions. The Schr\" odinger space-time can be obtained by the standard wave generating technique along one of the brane directions (for single brane) or one of the common brane directions (for intersecting branes) and then interchanging the light-cone coordinates by double Wick rotations, whereas, the Lifshitz space-time can be obtained by dimensionally reducing (for M-theory) along the wave direction or taking T-duality (for string theory) along the same direction. We thus obtain Schr\" odinger/Lifshitz dual space-times without or with hyperscaling violation from the same M/string theory solutions and they preserve some fraction of the supersymmetry.

30 pages, no figures; v2: typos corrected, added references, added acknowledgement; v3: added more references, acknowledgement and a note, added more clarifications, version to appear in JHEP

References in corpus (14)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Lectures on Holographic Superfluidity and Superconductivity
• Topological Order and Conformal Quantum Critical Points
• Nonrelativistic conformal field theories
• Lifshitz Solutions of D=10 and D=11 supergravity
• Wrapped M5-branes, consistent truncations and AdS/CMT
• Constructing Lifshitz solutions from AdS
• Lifshitz solutions in supergravity and string theory
• On bipartite Rokhsar-Kivelson points and Cantor deconfinement
• Special limits and non-relativistic solutions
• Supersymmetric solutions for non-relativistic holography
• Non-relativistic Branes
• Critical speeding-up in a local dynamics for the random-cluster model

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• Interpolating solution from AdS${}_5$ to hyperscaling violating Lifshitz space-time
• On a lightlike limit of entanglement
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