For unitary matrix models with potentials up to cos 3α, the paper infers phase diagrams from classical potential shape and shows beta functions on critical lines are nowhere vanishing, claiming third-order transitions.
The Quiver Matrix Model and 2d-4d Conformal Connection
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abstract
We review the quiver matrix model (the ITEP model) in the light of the recent progress on 2d-4d connection of conformal field theories, in particular, on the relation between Toda field theories and a class of quiver superconformal gauge theories. On the basis of the CFT representation of the beta deformation of the model, a quantum spectral curve is introduced as << det (x- i g_s \partial \phi(z)) >>=0 at finite N and for beta \neq 1. The planar loop equation in the large N limit follows with the aid of W_n constraints. Residue analysis is provided both for the curve of the matrix model with the "multi-log" potential and for the Seiberg-Witten curve in the case of SU(n) with 2n flavors, leading to the matching of the mass parameters. The isomorphism of the two curves is made manifest.
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Notes on phase structure and non-vanishing $\beta$ functions of one-unitary matrix model
For unitary matrix models with potentials up to cos 3α, the paper infers phase diagrams from classical potential shape and shows beta functions on critical lines are nowhere vanishing, claiming third-order transitions.