Large-N behavior of the Wilson loops of generalized two-dimensional Yang-Mills theories

TL;DR

This paper investigates the large-N limit of Wilson loop expectation values in two-dimensional Yang-Mills theories, revealing exponential behavior at large areas and phase transition features at critical areas.

Contribution

It provides a detailed analysis of Wilson loop behavior in generalized 2D Yang-Mills theories, highlighting phase transition phenomena and large-area asymptotics.

Findings

Wilson loops decay exponentially with area at large areas

Discontinuity in second derivative of Wilson loops at critical area

Behavior consistent across generalized Yang-Mills theories

Abstract

The large-N limit of the expectation values of the Wilson loops corresponding to two-dimensional U(N) Yang-Mills and generalized Yang-Mills theories on a sphere are studied. The behavior of the expectation values of the Wilson loops both near the critical area and for large areas are investigated. It is shown that the expectation values of the Wilson loops at large areas behave exponentially with respect to the area of the smaller region the boundary of which is the loop; and for the so called typical theories, the expectation values of the Wilson loops exhibit a discontinuity in their second derivative (with respect to the area) at the critical area.