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 $\lambda$ and the Veneziano parameter $\tau$. We compute the expectation value of Wilson loops in both phases, showing that the transition is third-order. A calculation of the $\beta$ function shows the existence of an IR stable fixed point.

19 pages

References in corpus (8)

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• A Study of U(N) Lattice Gauge Theory in 2-dimensions
• Wilson loops in unitary matrix models at finite $N$
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• Large $N$ expansion of Wilson loops in the Gross-Witten-Wadia matrix model

Cited by in corpus (3)

• Multiple phases and meromorphic deformations of unitary matrix models
• Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories
• 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