Neutral Multi-Instanton as a Bridge from Weak to Strong Coupling phase in Two Dimensional QCD

Details Neutral Multi-Instanton as a Bridge from Weak to Strong Coupling phase in Two Dimensional QCD Neutral Multi-Instanton as a Bridge from Weak to Strong Coupling phase in Two Dimensional QCD

1995-12-04

arxiv.org/abs/hep-th/9512009v1

Physics

High Energy Physics

High Energy Physics - Theory

26pages, Latex, 7 Postscript figures included by epsf

Scientific paper

Using a contour integral representation we analyze the multi-instanton sector in two dimensional $U(N)$ Yang-Mills theory on a sphere and argue the role of multi-instanton in the large $N$ phase transition. In the strong coupling region at the large $N$ , we encounter ``singular saddle point''. Because of this situation, ``neutral'' configurations of the multi-instanton are dominant in this region. Based on the ``neutral'' multi-instanton approximation we numerically calculate the multi-instanton amplitude , the free energies and the Wilson loops for finite $N$ . We also compare our results with the large $N$ exact solution of the free energy and the Wilson loop and argue some problems. We find the ``neutral'' multi-instanton contribution bridges the gap between weak and strong coupling phase.

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