Abstract
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.
Highlights
The study of Quantum Field Theory in different dimensions is compelling for several reasons
For concreteness we focus on maximally supersymmetric Yang-Mills, but our results apply to a larger class of theories with or without supersymmetry
For concreteness, in most of the paper we will focus on the simple cases of1 d = p + 1 dimensional, SU(N ), maximally supersymmetric super Yang-Mills (SYM) gauge theories that are realized on the worldvolume of N coincident Dp-branes in type II string theory [2]
Summary
The study of Quantum Field Theory in different dimensions is compelling for several reasons. In the case of strongly coupled systems with a finite density of quarks or electrons, the number of nonperturbative tools is very limited In this context, the gauge/string duality [1] provides a stimulating set of toy models in which a first-principle description is possible. We will show that the resulting dual solutions describe renormalization group (RG) flows towards infrared (IR) geometries characterized by fixed dynamical and hyperscaling-violating exponents The former arises by an explicit breaking of Lorentz-symmetry due to the presence of a charge density, whereas the latter indicates that dimensionful quantities besides the temperature enter in thermodynamics. For very small (large) values of the quark density the validity of the type II solution breaks down due to the dilaton becoming large In these cases one needs a dual description (an S-dual one in Type IIB and an uplift to M-theory in Type IIA) to correctly describe the strongly coupled system. In the appendix we give technical details on how to write a truncated action describing 10D supergravity in the presence of the string sources
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