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(Super)Yang-Mills at Finite Heavy-Quark Density

We study the gravitational duals of $d$-dimensional Yang-Mills theories with $d\leq 6$ in the presence of an ${\cal O} (N^2)$ density of heavy quarks, with $N$ the number of colors. For concreteness we focus on maximally supersymmetric Yang-Mills, but our results apply to a larger class of theories with or without supersymmetry. The gravitational solutions describe renormalization group flows towards infrared scaling geometries characterized by fixed dynamical and hyperscaling-violating exponents. The special case $d=5$ yields an $AdS_3 \times \mathbb{R}^4 \times S^4$ geometry upon uplifting to M-theory. We discuss the multitude of physical scales that separate different dynamical regimes along the flows, as well as the validity of the supergravity description. We also present exact black brane solutions that encode the low-temperature thermodynamics.