  We argue that there is a phase transition in the expectation value of the
Polyakov loop operator in the large N limit of the high temperature deconfined
phase of N=4 Yang-Mills theory on a spatial S^3. It occurs for large completely
symmetric representation of the SU(N) symmetry group. We speculate that this
transition is reflected in the string theory dual as a critical behavior of the
D3-brane duals of large representation loops.
