Topology-changing first order phase transition and the dynamics of flavor

In studying the dynamics of large $N_c$, $SU(N_c)$ gauge theory at finite temperature with fundamental quark flavors 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, ${\mathrm{AdS}}_5\mathrm{\text{−}}\mathrm{\text{Schwarzschild}}\times S^5$, probed by a D7-brane. The D7-brane has topology ${\mathbb{R}}^4\times S^3\times S^1$ 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.

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 $\varphi$. 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

Four-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.