Multiple phases and meromorphic deformations of unitary matrix models

We study a unitary matrix model with Gross-Witten-Wadia weight function and determinant insertions. After some exact evaluations, we characterize the intricate phase diagram. There are five possible phases: an ungapped phase, two different one-cut gapped phases and two other two-cut gapped phases. The transition from the ungapped phase to any gapped phase is third order, but the transition between any one-cut and any two-cut phase is second order. The physics of tunneling from a metastable vacuum to a stable one and of different releases of instantons is discussed. Wilson loops, $\beta$-functions and aspects of chiral symmetry breaking are investigated as well. Furthermore, we study in detail the meromorphic deformation of a general class of unitary matrix models, in which the integration contour is not anchored to the unit circle. The ensuing phase diagram is characterized by symplectic singularities and captured by a Hasse diagram.