Unitary Integrals and Related Matrix Models

On local gamma factors for orthogonal groups and unitary groups

‎In this paper‎, ‎we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for‎ ‎irreducible admissible representations of orthogonal groups‎, ‎or unitary groups‎. ‎One family is that of local integrals of the doubling method‎, ‎and the other family is‎ ‎that of local integrals expressed in terms of sph...

A New Construction of the Penner Model

The free energy of the Penner model is shown to be closely related to the integral over the two diagonalizing unitary matrices of a complex rectangular matrix. Matrix models1 can be solved if and only if the original integrals over matrix elements can be reduced to integrals over eigenvalues2,3. In these models, the “angular” integrals over the diagonalizing unitary matrices result in a numeric...

Unitary Matrix Models and 2D Quantum Gravity

The KdV and modified KdV integrable hierarchies are shown to be different descriptions of the same 2D gravitational system – open-closed string theory. Nonperturbative solutions of the multi-critical unitary matrix models map to nonsingular solutions of the ‘renormalisation group’ equation for the string susceptibility, [P̃ , Q] =Q . We also demonstrate that the large N solutions of unitary matr...

2-matrix versus complex matrix model, integrals over the unitary group as triangular integrals

Unitary matrix integrals in the framework of Generalized Kontsevich Model 1 . Brezin - Gross - Witten Model

We advocate a new approach to the study of unitary matrix models in external fields which emphasizes their relationship to Generalized Kontsevich Models (GKM) with non-polynomial potentials. For example, we show that the partition function of the Brezin-Gross-Witten Model (BGWM), which is defined as an integral over unitary N ×N matrices, ∫ [dU ]eTr(J†U+JU†), can also be considered as a GKM wit...