Hot Holographic Giant Loop

We consider the Polyakov loop operator in finite temperature planar N = 4 supersymmetric Yang-Mills theory defined on a spatial S3 and in representations where the number of boxes in the Young Tableau k is large and scales so that kN remains finite in the large N limit. We review the argument that, in the de-confined phase of the gauge theory, and for symmetric representations with row Young tableau, there is a quantum phase transition in the expectation value of the Polyakov loop operator which occurs as the size of the representation is increased beyond a critical value of kN. We also argue that for completely antisymmetric representations with column tableau, there is no such phase transition. The AdS/CFT dual of such large representation loops are thought to be probe D-branes with k units of fundamental string charge dissolved in their world-volumes. Our results for both symmetric and antisymmetric representations are consistent with what is known about these branes on the thermal AdS black hole background.