Lifshitz Solitons

TL;DR

This paper numerically constructs Lifshitz soliton solutions in higher-dimensional Einstein gravity coupled with massive gauge fields, revealing specific charge density values for Lifshitz asymptotics at certain critical exponents.

Contribution

It introduces a numerical method to find Lifshitz solitons in higher dimensions and identifies discrete charge values for specific Lifshitz scaling exponents.

Findings

Discrete magic charge values exist for z=2 in all dimensions n≥3.

Single magic charge value found for 1<z<2.

No solutions for z>2 sufficiently.

Abstract

We numerically obtain a class of soliton solutions for Einstein gravity in $(n+1)$ dimensions coupled to massive abelian gauge fields and with a negative cosmological constant with Lifshitz asymptotic behaviour. We find that for all $n\geq3$, a discrete set of magic values for the charge density at the origin (guaranteeing an asymptotically Lifshitz geometry) exists when the critical exponent associated with the Lifshitz scaling is $z=2$; moreover, in all cases, a single magic value is obtained for essentially every $1<z<2$, yet none when $z>2$ sufficiently.