Charged Black Holes in Colored Lifshitz Spacetimes

TL;DR

This paper explores Einstein-Yang-Mills theories with cosmological constant in four and five dimensions, discovering colored Lifshitz solutions with specific dynamic exponents, analyzing scalar triplet wave equations, and constructing exact charged black hole solutions with thermodynamic properties.

Contribution

It introduces new colored Lifshitz solutions with specific dynamic exponents and constructs exact charged black holes in these backgrounds, extending the understanding of holography in non-AdS spacetimes.

Findings

Colored Lifshitz solutions with z>1 in 4D and 5D.

Color modifies dual operator scaling dimensions.

Exact electrically-charged black hole solutions with specific z values.

Abstract

We consider Einstein gravities coupled to a cosmological constant and $SU(2)$ Yang-Mills fields in four and five dimensions. We find that the theories admit colored Lifshitz solutions with dynamic exponents $z>1$. We study the wave equations of the $SU(2)$ scalar triplet in the bulk, and find that the vacuum color modifies the scaling dimensions of the dual operators. We also introduce a Maxwell field and construct exact solutions of electrically-charged black holes that asymptote to the $D=4$, $z=3$ and $D=5$, $z=4$ colored Lifshitz spacetimes. We derive the thermodynamical first law for general colored and charged Lifshitz black holes.