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.
Hot Holographic Giant Loop
GRIGNANI, Gianluca;
2013
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.