Multiple phases in a generalized Gross-Witten-Wadia matrix model

Abstract

We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

Multiple phases and meromorphic deformations of unitary matrix models

“…The matrix model (2.1) is a massive deformation of the model studied in [22,23]. Besides, (2.1) is a generalization of the celebrated Gross-Witten-Wadia (GWW) model [4,5] by determinant insertions, and reduces to it for K = 0 or µ → ∞.…”

“…It was observed in [22] that the massless theory with fermions, that is = +1 and µ = 1, shows a Fisher-Hartwig (FH) singularity. The theory with bosons, on the contrary, yields a singular matrix model in the massless case.…”

“…The theory with bosons, on the contrary, yields a singular matrix model in the massless case. 2 Here we recognize the singularities encountered in [22] as the remnants of the IR singularities due to massless fields, and resolve them via mass deformation.…”

“…As we have stressed, a core assumption of our analysis is |µ| > 1, and the massless limit |µ| → 1 + can only be taken at the end. Due to the non-analyticity for µ ∈ T, the resulting model will differ from a model with massless matter [22,23].…”

“…Remark 2.2. For the role of the mass as a regulator (for the FH singularities on the mathematical side, for the IR singularities on the field theory side), we do not expect the continuation from M to the sheet {µ = 1} × R 2 , studied in [22,23], to be analytic.…”