Asymptotic symmetries of Schr\"odinger spacetimes

Understand

We discuss the asymptotic symmetry algebra of the Schrodinger-invariant metrics in d+3 dimensions and its realization on finite temperature solutions of gravity coupled to matter fields.

• These solutions have been proposed as gravity backgrounds dual to non-relativistic CFTs with critical exponent z in d space dimensions.
• It is known that the Schrodinger algebra possesses an infinite-dimensional extension, the Schrodinger-Virasoro algebra.
• However, we show that the asymptotic symmetry algebra of Schrodinger spacetimes is only isomorphic to the exact symmetry group of the background.