Related papers: Unitary matrix integrals in the framework of Gener…
Earlier we explained that partition functions of various matrix models can be constructed from that of the cubic Kontsevich model, which, therefore, becomes a basic elementary building block in "M-theory" of matrix models. However, the less…
Concise review of the basic properties of unitary matrix integrals. They are studied with the help of the three matrix models: the ordinary unitary model, Brezin-Gross-Witten model and the Harish-Charndra-Itzykson-Zuber model. Especial…
The Brezin-Gross-Witten (BGW) model is one of the basic examples in the class of non-eigenvalue unitary matrix models. The generalized BGW tau-function $\tau_N$ was constructed from a one parametric deformation of the original BGW model…
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…
The generalized Kontsevich model (GKM) is a one-matrix model with arbitrary potential. Its partition function belongs to the KP hierarchy. When the potential is monomial, it is an $r$-reduced tau-function that governs the $r$-spin…
Generalized Kontsevich Matrix Model (GKMM) with a certain given potential is the partition function of $r$-spin intersection numbers. We represent this GKMM in terms of fermions and expand it in terms of the Schur polynomials by…
We represent the partition function of the Generalized Kontsevich Model (GKM) in the form of a Toda lattice $\tau$-function and discuss various implications of non-vanishing "negative"- and "zero"-time variables: the appear to modify the…
We look for the origins of the single equation, which is a peculiar combination of W-constrains, which provides the non-abelian W-representation for generalized Kontsevich model (GKM), i.e. is enough to fix the partition function…
The Kazakov-Migdal model, if considered as a functional of external fields, can be always represented as an expansion over characters of $GL$ group. The integration over "matter fields" can be interpreted as going over the {\it model} (the…
In the recent study of Virasoro action on characters, we discovered that it gets especially simple for peculiar linear combinations of the Virasoro operators: particular harmonics of $\hat w$-operators. In this letter, we demonstrate that…
The generating functions for the gauge theory observables are often represented in terms of the unitary matrix integrals. In this work, the perturbative and non-perturbative aspects of the generic multi-critical unitary matrix models are…
We investigate the G/G gauged Wess-Zumino-Witten model on a Riemann surface from the point of view of the algebraic Bethe Ansatz for the phase model. After localization procedure is applied to the G/G gauged Wess-Zumino-Witten model, the…
We propose the Kazakov-Migdal model on graphs and show that, when the parameters of this model are appropriately tuned, the partition function is represented by the unitary matrix integral of an extended Ihara zeta function, which has a…
The Brezin-Gross-Witten tau function is a tau function of the KdV hierarchy which arises in the weak coupling phase of the Brezin-Gross-Witten model. It falls within the family of generalized Kontsevich matrix integrals, and its…
We review some relations occurring between the combinatorial intersection theory on the moduli spaces of stable curves and the asymptotic behavior of the 't Hooft-Kontsevich matrix integrals. In particular, we give an alternative proof of…
We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one can reduce the matrix integral to the…
In this paper, we examine a modification of the Kazakov-Migdal (KM) model with gauge group $U(N_c)$, where the adjoint scalar fields in the conventional KM model are replaced by $N_f$ fundamental scalar fields (FKM model). After tuning the…
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…
The open intersection theory has been initiated by R. Pandharipande, J. P. Solomon and R. J. Tessler. In the scope of matrix model theory, A. Buryak and R. J. Tessler have constructed a matrix model $\mathcal{Z}^o$ for the open partition…
Unitarity triangles and characteristic measurables of the $3\times 3$ Cabibbo-Kobayashi-Maskawa (CKM) matrix are discussed. Beyond the $3\times 3$ CKM scheme we make a rephasing-invariant generalization of the Gronau-Wyler-Dunietz approach…