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.
@article{arxiv.0904.3750,
title = {Hot Giant Loop Holography},
author = {Gianluca Grignani and Joanna L. Karczmarek and Gordon W. Semenoff},
journal= {arXiv preprint arXiv:0904.3750},
year = {2014}
}