From AdS to Schr\"odinger/Lifshitz dual space-times without or with hyperscaling violation

TL;DR

The paper demonstrates how intersecting branes in M/string theory can generate Schr"odinger and Lifshitz dual space-times, with a consistent relation between their dynamical exponents, using solution generating techniques and dimensional reduction.

Contribution

It introduces a unified method to derive Schr"odinger and Lifshitz space-times from M/string theory branes, revealing a fixed sum of their dynamical exponents and preserving supersymmetry.

Findings

Dynamical exponents of Schr"odinger and Lifshitz space-times sum to 2.

Multiple examples including M2-, M5-branes and D-branes are analyzed.

Dual space-times can be obtained with or without 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 ($p\neq 4$, 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.