Thermodynamics of AdS/QCD

TL;DR

The paper develops a phenomenological AdS/QCD model with two deformed 5D geometries and a dilaton to capture finite-temperature QCD-like thermodynamics. By fixing the deformation parameters with $T_c$ and the hadron spectrum, it demonstrates a consistent match between the boundary confinement-deconfinement transition and the bulk Hawking-Page transition, and it shows the quark-antiquark potential behaves as confining at $T=0$ and deconfined with entropy $\approx 2.1$ per pair for $T>T_c$. The work furnishes a coherent holographic description of the QCD phase structure, including an approximate Cornell-like potential and string-breaking behavior, while acknowledging the model's phenomenological nature and UV/IR sensitivities. This approach yields semi-quantitative agreement with lattice-scale expectations and motivates further top-down embedding and inclusion of dynamical flavors.

Abstract

We study finite temperature properties of four dimensional QCD-like gauge theories in the gauge theory/gravity duality picture. The gravity dual contains two deformed 5d AdS metrics, with and without a black hole, and a dilaton. We study the thermodynamics of the 4d boundary theory and constrain the two metrics so that they correspond to a high and a low temperature phase separated by a first order phase transition. The equation of state has the standard form for the pressure of a strongly coupled fluid modified by a vacuum energy, a bag constant. We determine the parameters of the deformation by using QCD results for $T_c$ and the hadron spectrum. With these parameters, we show that the phase transition in the 4d boundary theory and the 5d bulk Hawking-Page transition agree. We probe the dynamics of the two phases by computing the quark-antiquark free energy in them and confirm that the transition corresponds to confinement-deconfinement transition.

Figures (6)

• Figure 1: A plot of $w(z)$ defined by Eq.(\ref{['trialw']}) (left) and a plot of the low $T$ metric string frame deformation $f(z)=29[w(\sqrt{c}z)-w(\infty)]cz^2/20$, $c=0.127$ GeV$^2$, $w(\infty)=-1$.
• Figure 2: The pressure $p(T)$ and entropy density $s(T)=p'(T)$ in terms of temperature $T$ with $B=29 c^2N_c^2/(32\pi^2)$ and $L=T_c \Delta s=29 N_c^2 c^2/( 8 \pi^2)$. The contribution of the matter fields is neglected here, $C_m\ll c^2$.
• Figure 3: The difference $S^E_h - S^E_l$ between the actions computed with the metrics (\ref{['hightempmetric']}) and (\ref{['lowtempmetric']}). The difference vanishes at $T\approx0.181$ GeV, above that $S^E_h < S^E_l$ and the high $T$ metric (\ref{['hightempmetric']}) dominates.
• Figure 4: Three types of solutions: a $Q\bar{Q}$ solution (left), a solution with $z'=0$ only at $z=z_*$ (middle), a solution with a constant piece at $z=z_*$ (right).
• Figure 5: The functions $q(z)$ in Eq.(\ref{['gzh']}) and $L(z_*)$ in Eq.(\ref{['L']}) for the high temperature metric with $T=400 {\rm MeV}$ using the deformation (\ref{['fhz']}) (upper two panels). The lower two panels show the same for the low temperature metric with $T=0$, now plotted vs $z$ in units of 1/GeV.