Critical scaling in the matrix model on the Bethe tree

Details Critical scaling in the matrix model on the Bethe tree Critical scaling in the matrix model on the Bethe tree

1993-09-18

arxiv.org/abs/hep-th/9309100v1

Mod. Phys. Lett. A9 (1994) 1963-1974

Physics

High Energy Physics

High Energy Physics - Theory

12 pp., NBI-93-55

Scientific paper

The matrix model with a Bethe-tree embedding space (coinciding at large $N$ with the Kazakov-Migdal ``induced QCD'' model \cite{KM}) is investigated. We further elaborate the Riemann-Hilbert approach of \rf{Mig1} assuming certain holomorphic properties of the solution. The critical scaling (an edge singularity of the density) is found to be $\gamma_{str} = -\frac{1}{\pi} \arcos D$, for $|D|<1$, and $\gamma_{str} = -\frac{1}{\pi} \arcos \frac{D}{2D-1}$, for $D>1$. Explicit solutions are constructed at $D=\frac{1}{2}$ and $D=\infty$.

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