Heavy quark density in $ \mathcal{N} $ = 4 SYM: from hedgehog to Lifshitz spacetimes

Abstract

We study the effect of an O(N 2) density of heavy quarks in strongly coupled $ \mathcal{N} $ = 4 SUSY Yang-Mills theory in the large N limit. This is achieved in the type IIB supergravity dual by introducing a uniformly smeared density of macroscopic string sources stretching to the boundary of AdS 5 × S 5. The backreacted system exhibits a flow from an AdS 5 “hedgehog” geometry to a scaling Lifshitz-like solution Lif5 × S 5 with dynamical critical exponent z = 7, wherein the scaling symmetry is broken by a logarithmic running dilaton. We find an exact black brane solution within the scaling regime which describes the low temperature thermodynamics of the system.