Non-relativistic Hybrid Geometry with Gravitational Gauge-Fixing Term

TL;DR

This paper constructs a gravitational model that interpolates between Schrödinger and Lifshitz spacetimes, providing a potential holographic dual for non-relativistic boundary systems using a gauge-fixed Einstein-Maxwell-Higgs framework.

Contribution

It introduces a non-relativistic hybrid geometry solution supported by a gauge-fixing term, extending previous work on flow equations in holography.

Findings

Supports hybrid geometry with Einstein-Maxwell-Higgs system

Uses gauge-fixing for diffeomorphism to verify solutions

Proposes holographic dual for non-relativistic systems

Abstract

We search a gravitational system which allows a non-relativistic hybrid geometry interpolating the Schr\"odinger and Lifshitz spacetimes as a solution, as a continuation of the previous work employing a flow equation. As such a candidate an Einstein-Maxwell-Higgs system naturally arises and we verify that this system indeed supports the hybrid geometry with the help of a gauge-fixing term for diffeomorphism. As a result, this gravitational system may be interpreted as a holographic dual of a general non-relativistic system at the boundary.