Asymptotically Schroedinger Space-Times: TsT Transformations and Thermodynamics

Abstract

We study the complete class of 5-dimensional asymptotically Schroedinger space-times that can be obtained as the TsT transform of a 5-dimensional asymptotically AdS space-time. Based on this we identify a conformal class of Schroedinger boundaries. We use a Fefferman-Graham type expansion to study the on-shell action for this class of asymptotically Schroedinger space-times and we show that its value is TsT invariant. In the second part we focus on black hole space-times and prove that black hole thermodynamics is also TsT invariant. We use this knowledge to argue that thermal global Schroedinger space-time at finite chemical potential undergoes a Hawking-Page type phase transition.

References added

References in corpus (12)

• Many-Body Physics with Ultracold Gases
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Nonrelativistic conformal field theories
• Holographic stress tensor for non-relativistic theories
• Type IIB supergravity on squashed Sasaki-Einstein manifolds
• Correlation Functions in Non-Relativistic Holography
• Correlation functions in the non-relativistic AdS/CFT correspondence
• Thermodynamics of Black Holes in Schroedinger Space
• Geometry of Schroedinger Space-Times, Global Coordinates, and Harmonic Trapping
• Non-relativistic metrics with extremal limits
• Holographic real-time non-relativistic correlators at zero and finite temperature