Delayed Deconfinement and the Hawking-Page Transition

TL;DR

This paper introduces the concept of delayed deconfinement in complex matrix models, revealing a first-order transition in $ ext{N}=4$ SYM that aligns with gravity predictions, and explains the mismatch in black hole microstate counting.

Contribution

It demonstrates the phenomenon of delayed deconfinement in complex matrix models and applies it to $ ext{N}=4$ SYM, providing a new perspective on the confinement/deconfinement transition.

Findings

Delayed deconfinement leads to a first-order transition.

The deconfinement line matches gravity predictions.

Results extend to complex couplings in the Gross-Witten-Wadia model.

Abstract

We revisit the confinement/deconfinement transition in $\mathcal{N}=4$ super Yang-Mills (SYM) theory and its relation to the Hawking-Page transition in gravity. Recently there has been substantial progress on counting the microstates of 1/16-BPS extremal black holes. However, there is presently a mismatch between the Hawking-Page transition and its avatar in $\mathcal{N}=4$ SYM. This led to speculations about the existence of new gravitational saddles that would resolve the mismatch. Here we exhibit a phenomenon in complex matrix models which we call "delayed deconfinement". It turns out that when the action is complex, due to destructive interference, tachyonic modes do not necessarily condense. We demonstrate this phenomenon in ordinary integrals, a simple unitary matrix model, and finally in the context of $\mathcal{N}=4$ SYM. Delayed deconfinement implies a first-order transition, in contrast to the more familiar cases of higher-order transitions in unitary matrix models. We determine the deconfinement line and find remarkable agreement with the prediction of gravity. On the way, we derive some results about the Gross-Witten-Wadia model with complex couplings. Our techniques apply to a wide variety of (SUSY and non-SUSY) gauge theories though in this paper we only discuss the case of $\mathcal{N}=4$ SYM.