Phases of unitary matrix models and lattice QCD2

Abstract

We investigate the different large N phases of a generalized Gross-Witten-Wadia U (N ) matrix model. The deformation mimics the one-loop determinant of fermion matter with a particular coupling to gauge fields. In one version of the model, the GWW phase transition is smoothed out and it becomes a crossover. In another version, the phase transition occurs along a critical line in the two-dimensional parameter space spanned by the 't Hooft coupling λ and the Veneziano parameter τ . We compute the expectation value of Wilson loops in both phases, showing that the transition is third-order. A calculation of the β function shows the existence of an IR stable fixed point.

Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories

“…It is known that the unitary matrix models with general coupling have many phases [73,74,75,76,77]. We have considered the multi-critical models with real coupling g, and showed that they have three phases.…”

Construction of irregular conformal/W block and flavor mass relations of $\mathcal{N}=2$ SUSY gauge theory from the $A_{n-1}$ quiver matrix model

“…In the series of developments on the irregular limit of the A 1 (one-matrix) case [35][36][37][38][39][40][41], we have been led to the procedure of converting the hermitean matrix model into the unitary matrix model in order to make such procedure well-defined. The upshot from the case of N f = 2 is the well-known GWW model [42][43][44][45] (see also [46][47][48][49] for recent discussion) augmented by the log potential. The Painlevé II equation with parameter has been derived in the double scaling limit [35][36][37].…”