Three-dimensional super Yang-Mills with compressible quark matter

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We construct the gravity dual of three-dimensional, SU(Nc) super Yang-Mills theory with Nf flavors of dynamical quarks in the presence of a non-zero quark density Nq. The supergravity solutions include the backreaction of Nc color D2-branes and Nf flavor D6-branes with Nq units of electric flux on their worldvolume. For massless quarks, the solutions depend non-trivially only on the dimensionless combination ρ=Nc² Nq / λ² Nf⁴, with λ=gYM² Nc the 't Hooft coupling, and describe renormalization group flows between the super Yang-Mills theory in the ultraviolet and a non-relativistic theory in the infrared. The latter is dual to a hyperscaling-violating, Lifshitz-like geometry with dynamical and hyperscaling-violating exponents z=5 and θ=1, respectively. If ρ≪ 1 then at intermediate energies there is also an approximate AdS₄ region, dual to a conformal Chern-Simons-Matter theory, in which the flow exhibits quasi-conformal dynamics. At zero temperature we compute the chemical potential and the equation of state and extract the speed of sound. At low temperature we compute the entropy density and extract the number of low-energy degrees of freedom. For quarks of non-zero mass Mq the physics depends non-trivially on ρ and Mq Nc/λNf.