Chiral Transition of N=4 Super Yang-Mills with Flavor on a 3-Sphere

TL;DR

Using AdS/CFT, the authors numerically analyze a phase transition in large-$N_c$ ${\cal N}=4$ SYM on a 3-sphere with a finite number of massive ${\cal N}=2$ hypermultiplets, realized as $N_f$ probe D7-branes in $AdS_5\times S^5$. They perform holographic renormalization to extract the quark mass and chiral condensate and map the phase diagram in the $(m,T)$ plane, finding a first-order chiral transition line that appears only for $T$ above the Hawking-Page deconfinement temperature $T_{HP}$. In curved, finite-volume setups, the high-temperature behavior reproduces the flat-space result with a slope around $\approx 5.8$ (compared to $\approx 4.1$ in flat space after accounting for a $z$-coordinate rescaling), while no first-order transition is seen below $T_{HP}$ despite a bulk topology change. The work clarifies how deconfinement and flavor dynamics interplay in the large-$N_c$ limit on $S^3$ and suggests extensions to chemical potentials and backreaction.

Abstract

We use the AdS/CFT correspondence to perform a numerical study of a phase transition in strongly-coupled large-Nc N = 4 Super-Yang-Mills theory on a 3-sphere coupled to a finite number Nf of massive N = 2 hypermultiplets in the fundamental representation of the gauge group. The gravity dual system is a number Nf of probe D7-branes embedded in AdS_5 x S^5. We draw the phase diagram for this theory in the plane of hypermultiplet mass versus temperature and identify for temperatures above the Hawking-Page deconfinement temperature a first-order phase transition line across which the chiral condensate jumps discontinuously.

Figures (9)

• Figure 1: (a.) Phase Diagram of QCD with $N_c = 3$, $N_f = 2+1$ (b.) $N_c \rightarrow \infty$, $N_f = 2+1$
• Figure 2: The phase diagram for flavored ${\mathcal{N}} = 4$ Super-Yang Mills on a sphere as a function of temperature and hyper mass.
• Figure 3: (a.) Chiral Condensate as a function of mass ($M=1$); gray and black curves indicate solutions ending inside and outside the horizon respectively (b.) Close-up view of (a.)
• Figure 4: (a.) Free Energy as a function of mass ($M=1$). (b.) Close-up view of (a.)
• Figure 5: Phase Diagram of the ${\mathcal{N}} = 2$ theory in flat space. $T = M / \pi$.