Anisotropic scaling non-relativistic holography: a symmetry perspective

TL;DR

This paper explores the holographic duality of a 2D non-relativistic conformal field theory with anisotropic scaling, constructing a new 4D spacetime solution that exhibits the expected symmetry correspondence.

Contribution

It introduces a new 4D metric with global anisotropic scaling symmetry as a holographic dual for the 2D non-relativistic CFT, linking gravity and field theory symmetries.

Findings

The 4D spacetime is a homogeneous solution of Einstein gravity with quadratic-curvature extension.

The asymptotic symmetry matches the local anisotropic conformal symmetry of the dual field theory.

The constructed spacetime successfully captures the anisotropic scaling symmetry from a gravity perspective.

Abstract

We study the holographic dual of the two dimensional non-relativistic conformal field theory with anisotropic scaling from a symmetry perspective. We construct a new four dimensional metric with two dimensional global anisotropic scaling isometry. The four dimensional spacetime is homogeneous and is a solution of Einstein gravity with quadratic-curvature extension. We consider this spacetime dual to the vacuum of the conformal field theory. By introducing proper solution phase space, we find that the asymptotic symmetry of the gravity theory is the two dimensional local anisotropic conformal symmetry, which recovers precisely the results from the dual non-relativistic conformal field theory side.