Exploring Lovelock theory moduli space for Schroedinger solutions

TL;DR

This paper investigates the existence and properties of Schrödinger solutions within Lovelock gravity across various dimensions, revealing a special parameter space locus where such solutions exist with arbitrary radius and dynamical exponent.

Contribution

It characterizes the moduli space of Lovelock gravity where Schrödinger solutions are possible, including the special Chern-Simons subspace and its degeneracy features.

Findings

Schrödinger solutions exist on a co-dimension one locus in Lovelock parameter space.

On this locus, solutions have arbitrary radius and dynamical exponent z.

Degeneracy in configuration space persists under certain deformations.

Abstract

We look for Schroedinger solutions in Lovelock gravity in $D > 4$. We span the entire parameter space and determine parametric relations under which the Schroedinger solution exists. We find that in arbitrary dimensions pure Lovelock theories have Schroedinger solutions of arbitrary radius, on a co-dimension one locus in the Lovelock parameter space. This co-dimension one locus contains the subspace over which the Lovelock gravity can be written in the Chern-Simons form. Schroedinger solutions do not exist outside this locus and on this locus they exist for arbitrary dynamical exponent z. This freedom in z is due to the degeneracy in the configuration space. We show that this degeneracy survives certain deformation away from the Lovelock moduli space.