Thermodynamics of the brane

TL;DR

This work analyzes the thermodynamics and meson spectra of holographic gauge theories with a small number of fundamental flavors, modeled by D$q$-brane probes in black D$p$-brane backgrounds. A universal first-order phase transition at $T_{\rm fun}$ separates Minkowski (mesons bound) and black-hole (mesons melted) embeddings, with near-critical brane configurations exhibiting self-similarity and multiple embeddings. The authors compute free energy, entropy, energy, and the speed of sound for D3/D7 and D4/D6 systems, and reveal tachyonic instabilities of certain embeddings consistent with thermodynamic instability. Meson spectra on Minkowski embeddings show discrete, gapped states that become continuous and tachyonic near the transition, providing a gravity-side picture of meson melting in strongly coupled plasmas. Overall, the results connect brane embedding thermodynamics to meson dissociation, offering qualitative insights relevant to heavy-quark physics in QCD-like plasmas.

Abstract

The holographic dual of a finite-temperature gauge theory with a small number of flavours typically contains D-brane probes in a black hole background. We have recently shown that these systems undergo a first order phase transition characterised by a `melting' of the mesons. Here we extend our analysis of the thermodynamics of these systems by computing their free energy, entropy and energy densities, as well as the speed of sound. We also compute the meson spectrum for brane embeddings outside the horizon and find that tachyonic modes appear where this phase is expected to be unstable from thermodynamic considerations.