Macdonald's identities and the large N limit of $Y{M}_2$ on the cylinder

Abstract

We give a rigorous calculation of the large N limit of the partition function of SU(N) gauge theory on a 2D cylinder in the case where one boundary holomony is a so-called special element of type $\rho$. By MacDonald's identity, the partition function factors in this case as a product over positive roots and it is straightforward to calculate the large N asymptotics of the free energy. We obtain the unexpected result that the free energy in these cases is asymptotic to N times a functional of the limit densities of eigenvalues of the boundary holonomies. This appears to contradict the predictions of Gross-Matysin and Kazakov-Wynter that the free energy should have a limit governed by the complex Burgers equation.

Cited by in corpus (6)

• Brownian Motion, Chern-Simons Theory, and 2d Yang-Mills
• Large deviations and stochastic calculus for large random matrices
• Chern-Simons Theory in Lens Spaces from 2d Yang-Mills on the Cylinder
• Character expansion method for the first order asymptotics of a matrix integral
• Large $N$ behaviour of the two-dimensional Yang-Mills partition function
• A new large N phase transition in YM2