Quark-Antiquark Potential as a Probe for Holographic Phase Transitions

In the recent paper (Phys.Rev.Lett. 133 (2024) 12, 121601), a higher-order phase transition between the planar, charged, 5-dimensional Reissner-Nordstr\"om-Anti-de Sitter black hole and a hairy black hole solution of the type IIB supergravity was investigated. Here, following a bottom-up approach, we set out to investigate these two phases of the theory by means of the holographic probe that describes a quark-antiquark in the dual gauge theory. We ask ourselves whether studying the quark-antiquark potential suffices to detect the change of behavior at different values of the parameter that controls the phase transition, this parameter being the ratio between the chemical potential and the temperature. We show that, while evaluating the probe on both phases leads to the same value at the point where the transition takes place, there is always one phase that dominates over the other with regard to this observable. The same can be said about higher-dimensional probes such as those involved in the computation of holographic entanglement entropy.