A Topology-Changing Phase Transition and the Dynamics of Flavour

TL;DR

The paper presents a holographic study of a topology-changing, first-order phase transition in the flavor sector of a large-$N_c$ gauge theory at finite temperature, realized via a D7-brane probe in the $AdS_5$-Schwarzschild$\times S^5$ background. By solving the D7 embedding equation with an IR-focused shooting method, the authors identify two competing branches—$S^1$-vanishing (condensate) and $S^3$-vanishing (KK-like)—and locate a first-order transition at $m\approx 0.92345$ where the quark condensate $c$ jumps. The transition is encoded in the on-shell free energy and also leaves a signature in the meson spectrum, with condensate branches exhibiting quasinormal behavior while KK-like branches retain a discrete spectrum. The work illustrates how topology changes in probe branes map to phase structure in the dual gauge theory and motivates future studies including backreaction and $N_f\sim N_c$ effects to explore QCD-like universality classes.

Abstract

In studying the dynamics of large N_c, SU(N_c) gauge theory at finite temperature with fundamental quark flavours in the quenched approximation, we observe a first order phase transition. A quark condensate forms at finite quark mass, and the value of the condensate varies smoothly with the quark mass for generic regions in parameter space. At a particular value of the quark mass, there is a finite discontinuity in the condensate's vacuum expectation value, corresponding to a first order phase transition. We study the gauge theory via its string dual formulation using the AdS/CFT conjecture, the string dual being the near-horizon geometry of N_c D3-branes at finite temperature, AdS_5--Schwarzschild X S^5, probed by a D7-brane. The D7-brane has topology R^4 X S^3 X S^1 and allowed solutions correspond to either the S^3 or the S^1 shrinking away in the interior of the geometry. The phase transition represents a jump between branches of solutions having these two distinct D-brane topologies. The transition also appears in the meson spectrum.

Figures (5)

• Figure 1: Solutions for the D7--brane probe in the black hole background.
• Figure 2: Probe free energy (in units of $2 \pi \tau_7 N_f b/ R^2)$ and condensate vev at the phase transition. See text for more details.
• Figure 3: Four--dimensional meson mass $M$, as a function of fundamental quark mass $m$, from fluctuations in $\phi$. Only the first level of the discrete spectrum is shown. The blue (dashed) curves in (a) and (b) correspond to the meson mass before the meson melts.
• Figure 4: Four--dimensional meson mass $M$, as a function of fundamental quark mass $m$, from fluctuations in $\theta$. Only the first level of the discrete spectrum is shown. The blue (dashed) curves in (a) and (b) correspond to the meson mass before the meson melts.
• Figure 5: 4--dimensional meson mass $M$, as a function of fundamental quark mass $m$, from fluctuations in $A_b$. Only the first level of the discrete spectrum is shown. The blue (dashed) curves in (a) and (b) correspond to the meson mass before the meson melts.