Gyrating Schrodinger Geometries and Non-Relativistic Field Theories

TL;DR

This paper introduces new gyrating Schrödinger geometries as gravity duals to non-relativistic field theories with broken symmetry, including supersymmetric solutions and exact Green functions.

Contribution

It presents novel homogeneous metrics of Petrov type III describing gyrating Schrödinger geometries in various gravity theories, extending the holographic duality to more complex non-relativistic systems.

Findings

Gyrating Schrödinger solutions can be supersymmetric in Einstein-Weyl supergravity.

Exact Green functions are derived for bulk massive scalars in these geometries.

Solutions are applicable in four and higher-dimensional extended gravity theories.

Abstract

We propose homogeneous metrics of Petrov type III that describe gyrating Schrodinger geometries as duals to some non-relativistic field theories, in which the Schrodinger symmetry is broken further so that the phase space has a linear dependence of the momentum in a selected direction. We show that such solutions can arise in four-dimensional Einstein-Weyl supergravity as well as higher-dimensional extended gravities with quadratic curvature terms coupled to a massive vector. In Einstein-Weyl supergravity, the gyrating Schrodinger solutions can be supersymmetric, preserving 1/4 of the supersymmetry. We obtain the exact Green function in the phase space associated with a bulk free massive scalar.