Anti-de Sitter Black Hole Thermodynamics in Higher Derivative Gravity and New Confining-Deconfining Phases in dual CFT

TL;DR

This work analyzes five-dimensional AdS black hole thermodynamics in higher-derivative gravity, focusing on R^2-type corrections that introduce a parameter ε = c κ^2. It derives how the free energy, entropy, and temperature are modified, and shows that HD terms can shift or even reverse Hawking-Page transitions, yielding an N-dependent confinement/deconfinement structure in the dual ${ m N}=2$ Sp(N) SCFT. The results reveal a wealth of phase behavior, including ε/l^2–driven regimes and potential critical lines for more general HD actions, with implications for holographic modeling of confining gauge theories. Overall, the paper demonstrates that 1/N corrections captured by higher-derivative terms substantially enrich the phase diagram beyond Einstein gravity, linking gravity dynamics to finite-N effects in the dual CFT.

Abstract

The thermodynamics of d5 AdS BHs with positive, negative or zero curvature spatial section in higher derivative (HD) gravity is described. HD contribution to free energy may change its sign which leads to more complicated regime for Hawking-Page phase transitions. Some variant of d5 HD gravity is dual to ${\cal N}=2$ $Sp(N)$ SCFT up to the next-to-leading order in large $N$. Then, according to Witten interpretation the stable AdS BH phase corresponds to deconfinement while global AdS phase corresponds to confinement. Unlike to Einstein gravity in HD theory the critical $N$ appears. It may influence the phase transition structure. In particulary, what was confining phase above the critical value becomes the deconfining phase below it and vice-versa.