  Motivated by the warped conifold compactification, we model the infrared (IR)
dynamics of confining gauge theories in a Randall-Sundrum (RS)-like setup by
modifying the stabilizing Goldberger-Wise (GW) potential so that it becomes
large (in magnitude) in the IR and back-reacts on the geometry. We study the
high-temperature phase by considering a black brane background in which we
calculate the entropy and free energy of the strongly back-reacted solution. As
with Buchel's result for the conifold (arXiv:2103.15188), we find a minimum
temperature beyond which the black brane phase is thermodynamically unstable.
In the context of a phase transition to the confining background, our results
suggest that the amount of supercooling that the metastable black brane phase
undergoes can be limited. It also suggests the first-order phase transition
(and the associated gravitational waves from bubble collision) is not
universal. Our results therefore have important phenomenological implications
for early universe model building in these scenarios.
