Holographic Thermodynamics at Finite Baryon Density: Some Exact Results

Abstract

We use the AdS/CFT correspondence to study the thermodynamics of massive N=2 supersymmetric hypermultiplets coupled to N=4 supersymmetric SU(Nc) Yang-Mills theory in the limits of large Nc and large 't Hooft coupling. In particular, we study the theory at finite baryon number density. At zero temperature, we present an exact expression for the hypermultiplets' leading-order contribution to the free energy, and in the supergravity description we clarify which D-brane configuration is appropriate for any given value of the chemical potential. We find a second-order phase transition when the chemical potential equals the mass. At finite temperature, we present an exact expression for the hypermultiplets' leading-order contribution to the free energy at zero mass.

Figures (1)

• Figure 1: Cartoons of the allowed D7-brane embeddings at zero temperature. The vertical axis is one of the directions transverse to the D3-branes but parallel to the D7-branes. The horizontal axis is an overall transverse direction. (a.) A Minkowski embedding corresponding to $y(r)$ being constant. (b.) A $\frac{d^2}{(2\pi\alpha')^2} - c^2<0$ solution with turnaround describing a brane/anti-brane embedding as in ref. Herzog:2007kh. (c.) The zero-temperature $\frac{d^2}{(2\pi\alpha')^2} - c^2 >0$ horizon-crossing "black hole" embedding.