  We study the Cardy-like asymptotics of the 4d $\mathcal N=4$ index and
demonstrate the existence of partially deconfined phases where the asymptotic
growth of the index is not as rapid as in the fully deconfined case. We then
take the large-$N$ limit after the Cardy-like limit and make a conjecture for
the leading asymptotics of the index. While the Cardy-like behavior is derived
using the integral representation of the index, we demonstrate how the same
results can be obtained using the Bethe ansatz type approach as well. In doing
so, we discover new non-standard solutions to the elliptic Bethe ansatz
equations including continuous families of solutions for $SU(N)$ theory with
$N\ge3$. We argue that the existence of both standard and continuous
non-standard solutions has a natural interpretation in terms of vacua of
$\mathcal N=1^*$ theory on $\mathbb R^3\times S^1$.

High Energy Physics - Theory