The black hole in the throat - thermodynamics of strongly coupled cascading gauge theories

TL;DR

The authors numerically construct black hole solutions dual to the deconfined, chirally symmetric phase of strongly coupled cascading gauge theories and compute the free energy as a function of temperature. By solving a constrained system of five scalars in a five-dimensional effective theory, they map UV KT boundary data to field-theory observables and extract the stress tensor and scalar operator VEVs. They find a first-order deconfinement transition to the chirally symmetric phase at $T_{\text{critical}} = 0.614111(3)\,\Lambda$, with the transition characterized by a vanishing free energy and a regular horizon; at high temperatures the theory approaches conformal-like thermodynamics with calculable logs from the running of the cascade. The results provide a concrete holographic, non-conformal example of deconfinement and chiral-symmetry restoration, including quantitative thermodynamics, scaling relations, and operator expectations that can inform comparisons with QCD-like plasmas and hydrodynamic behavior.

Abstract

We numerically construct black hole solutions corresponding to the deconfined, chirally symmetric phase of strongly coupled cascading gauge theories at various temperatures. We compute the free energy as a function of the temperature, and we show that it becomes positive below some critical temperature, indicating the possibility of a first order phase transition at which the theory deconfines and restores the chiral symmetry.

Figures (13)

• Figure 1: Mismatch of $h_b(x)$ (for $x<0.5$) and $h_h(y\equiv 1-x)$ (for $x>0.5$) for different values of the parameters, for $k_s=0.4$. The solid (blue) curves correspond to "correct" values of the parameters \ref{['uvpar']} and \ref{['irrap']}, with $||\vec{v}_{mismatch}|| \approx 9\times 10^{-6}$. The dotted (green) curves corresponding to all values of parameters $10\%$ larger than the correct ones, produce $||\vec{v}_{mismatch}||\approx 3\times 10^{-1}$. The dashed (red) curves correspond to all values of parameters $20\%$ smaller than the correct ones, giving $||\vec{v}_{mismatch}||\approx 8\times 10^{-1}$.
• Figure 2: Values of the UV parameters $\hat{a}_{2,0}$ and $\hat{a}_{3,0}$ as a function of $k_s$ (blue points). The dashed/dotted (red/green) curves represent the perturbative ${\cal O}(k_s^{-1})$/${\cal O}(k_s^{-2})$ asymptotics of the parameters, given by \ref{['pert']}.
• Figure 3: Values of the UV parameters $\hat{a}_{4,0}$ and $g_{2,0}$ as a function of $k_s$ (blue points). The dashed/dotted (red/green) curves represent the perturbative ${\cal O}(k_s^{-1})$/${\cal O}(k_s^{-2})$ asymptotics of the parameters, given by \ref{['pert']}.
• Figure 4: The values of the UV parameters $\hat{a}_{2,0}$ and $\hat{a}_{3,0}$ as a function of $k_s$.
• Figure 5: The values of the UV parameters $\hat{a}_{4,0}$ and $g_{2,0}$ as a function of $k_s$.