Abstract

We use Polyakov loop eigenvalues to explore the phase diagram of BPS black holes in $AdS_5 \times S_5$, with the particular aim of understanding the holographic dual of the partially deconfined phase. We find evidence for an instability along the small black hole saddle at equal charges, indicated by the condensation of instantons in the superconformal index. This could resolve a paradox about the location of the Gross-Witten-Wadia transition in the black hole phase diagram, as well as indicate a richer phase diagram for $\mathcal N=4$ SYM and the BPS black holes in $AdS_5 \times S^5$. We discuss implications for the understanding of confinement and partial deconfinement – including a new prediction for the quark-gluon plasma – as well as for the BPS black hole phase diagram and the holographic representation of colour degrees of freedom.