Holographic phase transitions at finite chemical potential

TL;DR

This paper analyzes the finite- density phase structure of a holographic SU($N_c$) gauge theory with $N_f \ll N_c$ fundamental flavors by embedding $N_f$ D7-branes in the D3-brane black hole geometry. Using the grand canonical ensemble, it computes the D7-brane thermodynamics via the renormalized Euclidean action to map the phase diagram in $(T,\mu_q)$, distinguishing Minkowski embeddings (with $n_q=0$) from black hole embeddings (with $n_q\neq0$). The main finding is a line of first-order transitions for $\mu_q/M_q<1$ separating the low-temperature Minkowski phase from the high-temperature black hole phase; for $\mu_q/M_q>1$ no transition occurs and the black hole phase dominates at all $T$, with a critical point at $\mu_q/M_q=1$ where the transition becomes second order. The paper also discusses how the canonical ensemble at fixed $n_q$ exhibits an unstable region and how an inhomogeneous phase likely resolves the discrepancy between ensembles, offering insights into meson melting and quark excitations in strongly coupled plasmas and implications for QCD-like theories.

Abstract

Recently holographic techniques have been used to study the thermal properties of N=2 super-Yang-Mills theory, with gauge group SU(Nc) and coupled to Nf << Nc flavours of fundamental matter, at large Nc and large 't Hooft coupling. Here we consider the phase diagram as a function of temperature and baryon chemical potential mu. For fixed mu < Nc Mq there is a line of first order thermal phase transitions separating a region with vanishing baryon density and one with nonzero density. For fixed mu > Nc Mq there is no phase transition as a function of the temperature and the baryon density is always nonzero. We also compare the present results for the grand canonical ensemble with those for canonical ensemble in which the baryon density is held fixed [1].