Related papers: Large-N Reduction, Master Field and Loop Equations…
We study the large N asymptotics of the Brownian motions on the orthogonal, unitary and symplectic groups, extend the convergence in non-commutative distribution originally obtained by Biane for the unitary Brownian motion to the orthogonal…
The matrix model of Kapustin, Willett, and Yaakov is a powerful tool for exploring the properties of strongly interacting superconformal Chern-Simons theories in 2+1 dimensions. In this paper, we use this matrix model to study necklace…
We construct an effective model for the chiral field and the Polyakov loop in which we can investigate the interplay between the approximate chiral symmetry restoration and the deconfinement of color in a thermal SU(3) gauge theory with…
We study the single site SU(N) lattice gauge theory with N_f=2 adjoint Wilson fermions for values of N up to 53. We determine the phase diagram of the theory as a function of the hopping parameter kappa and the inverse 't Hooft coupling b,…
The space-time reduced model of large N QCD with two adjoint Wilson fermions is constructed by applying the symmetric twist boundary conditions with non-vanishing flux $k$. For large but finite $N=L^2$, the model should behave as the large…
Generalizations of QCD in which the number of colors N is taken to infinity are characterized by profound mathematical properties, with far-reaching implications for fundamental problems and for phenomenological issues alike. In this…
This thesis studies matrix field theories, which are a special type of matrix models. First, the different types of applications are pointed out, from (noncommutative) quantum field theory over 2-dimensional quantum gravity up to algebraic…
We apply the method of reduction of couplings in a Finite Unified Theory and in the MSSM. The method consists on searching for renormalization group invariant relations among couplings of a renormalizable theory holding to all orders in…
A construction of master field describing multicolour QCD is presented. The master fields for large N matrix theories satisfy to standard equations of relativistic field theory but fields are quantized according $q$-deformed commutation…
I review some recent works on the Hermitean one-matrix and d-dimensional gauge-invariant matrix models. Special attention is paid to solving the models at large-N by the loop equations. For the one-matrix model the main result concerns…
We review some of the basic features of the Kazakov-Migdal model of induced QCD. We emphasize the role of $Z_N$ symmetry in determining the observable properties of the model and also argue that it can be broken explicitly without ruining…
In Lagrangian gauge systems, the vector space of global reducibility parameters forms a module under the Lie algebra of symmetries of the action. Since the classification of global reducibility parameters is generically easier than the…
It is believed that fermions in adjoint representation on single site lattice will restore the center symmetry, which is a crucial requirement for the volume independence of large-N lattice gauge theories. We present a perturbative analysis…
We continue our analysis of the field strength correlation functions of two-dimensional QCD on Riemann surfaces by studying the large $N$ limit of these correlation functions on the sphere for gauge group $U(N)$. Our results allow us to…
We discuss the notion of a large field cutoff for lattice gauge models with compact groups. We propose and compare gauge invariant and gauge dependent (in the Landau gauge) criteria to sort the configurations into ``large-field'' and…
The relation between the Seiberg-Witten prepotentials, Nekrasov functions and matrix models is discussed. We derive quasiclassically the matrix models of Eguchi-Yang type, describing the instantonic contribution to the deformed partition…
We study four dimensional large-N SU(N) Yang-Mills theory coupled to adjoint overlap fermions on a single site lattice. Lattice simulations along with perturbation theory show that the bare quark mass has to be taken to zero as one takes…
The master field is the large $N$ limit of the Yang-Mills measure on the Euclidean plane. It can be viewed as a non-commutative process indexed by paths on the plane. We construct and study generalized master fields, called free planar…
We study cutoff and lattice effects in the O(n) symmetric $\phi^4$ theory for a $d$-dimensional cubic geometry of size $L$ with periodic boundary conditions. In the large-N limit above $T_c$, we show that $\phi^4$ field theory at finite…
For small values of the gauge coupling constant, we compare the densities of the energy of the vacuum and of the order parameter, evaluated in the lattice Monte Carlo simulation and in the perturbative field theory at two loop (Minkowski).…