Holographic phase transitions at finite baryon density

TL;DR

The paper investigates finite baryon density effects in a strongly coupled holographic gauge theory by embedding $N_f$ D7-branes into a black D3-brane background and turning on a worldvolume gauge field $A_t$ to introduce a chemical potential. Using a Legendre-transformed D7-brane action, they analyze embedding solutions $\chi(\rho)$, extract quark mass $m$ and condensate $c$, and map the finite-density physics to a phase diagram featuring a line of meson-melting transitions that ends at a critical point; Minkowski embeddings are excluded at finite density, and a density-dependent instability $(\partial \mu/\partial n_b)_T<0$ emerges in part of the diagram. A near-horizon spike interpretation identifies the density as a bundle of fundamental strings, providing a brane picture for constituent quarks at finite density and explaining why the transition persists only at small density and can disappear at larger density. The thermodynamics of the D7 sector, computed from renormalized Euclidean action and its Legendre transform, reveals a swallow-tail free-energy structure and a stability region that shapes the phase diagram, with potential new phases suggested by the instability. Collectively, the work clarifies how finite density modifies holographic meson physics in Dp/Dq systems and offers a concrete framework to compare with QCD-like phenomena at finite density.

Abstract

We use holographic techniques to study SU(Nc) super Yang-Mills theory coupled to Nf << Nc flavours of fundamental matter at finite temperature and baryon density. We focus on four dimensions, for which the dual description consists of Nf D7-branes in the background of Nc black D3-branes, but our results apply in other dimensions as well. A non-zero chemical potential mu or baryon number density n is introduced via a nonvanishing worldvolume gauge field on the D7-branes. Ref. [1] identified a first order phase transition at zero density associated with `melting' of the mesons. This extends to a line of phase transitions for small n, which terminates at a critical point at finite n. Investigation of the D7-branes' thermodynamics reveals that (d mu / dn)_T <0 in a small region of the phase diagram, indicating an instability. We comment on a possible new phase which may appear in this region.