Comments on k-Strings at Large N

TL;DR

This paper computes the k-string tension in large N two-dimensional lattice Yang-Mills theory, revealing phase transition behaviors, duality, and Casimir scaling in the continuum limit.

Contribution

It provides an explicit calculation of the interaction energy for k-strings at large N and analyzes phase transitions and duality in the model.

Findings

Interaction energy for k-strings is finite and attractive at large N.

The k -> N - k duality manifests as a first order phase transition.

Lattice k-string tension approaches Casimir scaling in the continuum limit.

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 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.