Comments on k-strings at large N

Abstract

We present a computation of the k-string tension in the large N limit of the two-dimensional lattice Yang-Mills theory. It is well known that the problems of computing the partition function and the Wilson loop can be both reduced to a unitary matrix integral which has a third order phase transition separating weak and strong coupling. We give an explicit computation of the interaction energy for k-strings in the large N limit when $ \frac{k}{N} $ is held constant and non-zero. In this limit, the interaction energy is finite and attractive. We show that, in the strong coupling phase, the k → N − k duality is realized as a first order phase transition. We also show that the lattice k-string tension reduces to the expected Casimir scaling in the continuum limit.