Holography and Thermodynamics of 5D Dilaton-gravity

TL;DR

This work develops a five‑dimensional Einstein–dilaton holographic model with a monotonic dilaton potential to emulate large‑N_c YM physics. By analyzing vacuum and finite‑temperature backgrounds, it proves the existence and uniqueness of black‑hole solutions for each horizon value and establishes a Hawking–Page–like confinement/deconfinement transition that is first order in confining theories and absent in non‑confining ones. The study reveals a deep link between the trace anomaly, the gluon condensate, and the deconfinement transition, and shows that at high temperature the thermodynamics approaches a free‑gluon gas with subleading logarithmic corrections. An axion sector captures topological aspects, predicting vanishing topological density in the deconfined phase. The reformulation in scalar variables $X(\

Abstract

The asymptotically-logarithmically-AdS black-hole solutions of 5D dilaton gravity with a monotonic dilaton potential are analyzed in detail. Such theories are holographically very close to pure Yang-Mills theory in four dimensions. The existence and uniqueness of black-hole solutions is shown. It is also shown that a Hawking-Page transition exists at finite temperature if and only if the potential corresponds to a confining theory. The physics of the transition matches in detail with that of deconfinement of the Yang-Mills theory. The high-temperature phase asymptotes to a free gluon gas at high temperature matching the expected behavior from asymptotic freedom. The thermal gluon condensate is calculated and shown to be crucial for the existence of a non-trivial deconfining transition. The condensate of the topological charge is shown to vanish in the deconfined phase.

Figures (16)

• Figure 1: Typical plots of the black-hole temperature (a) and free energy (b) as a function of the horizon position $r_h$, in a confining background. The temperature features a minimum at $r_{min}$ , that separates the large black-hole from the small black-hole branches.
• Figure 2: The temperature as a function of the horizon value of $\lambda$ in the model specified by the potential (\ref{['explicitV']}), for $Q=2/3$ and various values of $P$. The other coefficients are fixed to $V_1=10$, $V_2=100$. The confining models ($P>0$) feature a minimum temperature at finite $\lambda_h$; in the non-confining model ($P=-1$) the $T(\lambda_h)$ monotonically decreases to zero; In the borderline case ($P=0$) $T(\lambda_h)$ decreases monotonically to a finite value as $\lambda\to \infty$.
• Figure 3: Temperature as a function of (a) $r_h$ in the model (\ref{['explicitV']}) for $Q=2/3$ and $P=2$. The temperature diverges for $\lambda_h\to \infty$, for which $r_h\to r_0$. It is a single-valued function of $\lambda_h$, but not of $r_h$.
• Figure 4: Black hole free energy
• Figure 5: Temperature as a function of $\lambda_h$ for the infinite r geometries of the type $A\to r^{\alpha}$. Black holes exist only above $T_{min}$ whose precise value depend on the particular zero-$T$ geometry.