Three-dimensional super Yang-Mills with compressible quark matter

Abstract

We construct the gravity dual of three-dimensional, $SU(N_{\text{c}})$ super Yang-Mills theory with $N_{\text{f}}$ flavors of dynamical quarks in the presence of a non-zero quark density $N_{\text{q}}$. The supergravity solutions include the backreaction of $N_{\text{c}}$ color D2-branes and $N_{\text{f}}$ flavor D6-branes with $N_{\text{q}}$ units of electric flux on their worldvolume. For massless quarks, the solutions depend non-trivially only on the dimensionless combination $\rho =N_{\text{c}}^2{N}_{\text{q}}/{\lambda }^2{N}_{\text{f}}^4$, with $\lambda =g_{\text{YM}}^2{N}_{\text{c}}$ 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 $\theta =1$, respectively. If $\rho \ll 1$ then at intermediate energies there is also an approximate AdS${}_4$ 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 $M_{\text{q}}$ the physics depends non-trivially on $\rho$ and $M_{\text{q}}{N}_{\text{c}}/\lambda N_{\text{f}}$.

32 pages plus appendices, 11 figures

References in corpus (7)

• Effective Holographic Theories for low-temperature condensed matter systems
• Scaling theory of the cuprate strange metals
• D3-D7 Quark-Gluon Plasmas at Finite Baryon Density
• Conductivities for Hyperscaling Violating Geometries
• Nearly Kaehler Reduction
• Intermediate scalings in holographic RG flows and conductivities
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Cited by in corpus (11)

• Breaking the sound barrier in AdS/CFT
• Collective excitations of massive flavor branes
• Romans-mass-driven flows on the D2-brane
• (Super)Yang-Mills at Finite Heavy-Quark Density
• Towards a Holographic Quark Matter Crystal
• Holography with a Landau pole
• Unquenched flavor on the Higgs branch
• Quantum phase transitions with dynamical flavors
• Flavours and Infra-red Instability in Holography
• Fundamental Flavours, Fields and Fixed Points: A Brief Account
• Noisy Branes