Macdonald's identities and the large N limit of $YM_2$ on the cylinder

Details Macdonald's identities and the large N limit of $YM_2$ on the cylinder Macdonald's identities and the large N limit of $YM_2$ on the cylinder

2003-05-24

arxiv.org/abs/hep-th/0305218v1

Commun.Math.Phys. 245 (2004) 611-626

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1007/s00220-003-1027-x

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.

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