Abstract
We construct the gravity dual of d = 4, mathcal{N}=4 , SU(Nc) super Yang-Mills theory, coupled to Nf flavors of dynamical quarks, at non-zero temperature T and nonzero quark density Nq. The supergravity solutions possess a regular horizon if T > 0 and include the backreaction of Nc color D3-branes and Nf flavor D7-branes with Nq units of electric flux on their worldvolume. At zero temperature the solutions interpolate between a Landau pole singularity in the ultraviolet and a Lifshitz geometry in the infrared. At high temperature the thermodynamics is directly sensitive to the Landau pole, whereas at low temperature it is not, as expected from effective field theory. At low temperature and sufficiently high charge density we find thermodynamic and dynamic instabilities towards the spontaneous breaking of translation invariance.
Highlights
Duality, or holography for short [2,3,4], provides a framework in which the construction of such models is possible
At low temperature and sufficiently high charge density we find thermodynamic and dynamic instabilities towards the spontaneous breaking of translation invariance
We study holographically a family of theories consisting of super Yang-Mills (SYM) with Nc colors and Nf massless flavors at non-zero temperature T and non-zero charge density Nq
Summary
We study holographically a family of theories consisting of SYM with Nc colors and Nf massless flavors at non-zero temperature T and non-zero charge density Nq. The string dual to this configuration is given by the geometry sourced by a stack of type IIB Nc D3branes coupled to a set of Nf D7-branes with Nq units of electric flux on their worldvolume. We smear the D7-branes in these compact directions in the most symmetric way compatible with supersymmetry. In this way we recover some of the isometries that would be broken by a single D7-brane (or by a collection of overlapping D7-branes) and reduce the problem to solving ordinary (as opposed to partial) differential equations
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