Related papers: Large-N Reduction, Master Field and Loop Equations…
We study Markov perfect equilibria in continuous-time dynamic games with finitely many symmetric players. The corresponding Nash system reduces to the Nash-Lasry-Lions equation for the common value function, also known as the master…
An approach to studying lattice gauge models in the weak coupling region is proposed. Conceptually, it is based on the crucial role of the original Z(N) symmetry and the invariant gauge group measure. As an example, we calculate an…
The large-$N$ quantum field theories provide a window into the regime of strongly-coupled physics. Our principal object of study in this thesis is the large-$N$ family of melonic QFTs, which contain the Sachdev-Ye-Kitaev-like models, tensor…
The classical analysis of Kazakov and Kostov of the Makeenko-Migdal loop equation in two-dimensional gauge theory leads to usual partial differential equations with respect to the areas of windows formed by the loop. We extend this…
We investigate the QCD phase diagram by using the strong-coupling expansion of the lattice QCD with one species of staggered fermion and the Polyakov loop effective action at finite temperature (T) and quark chemical potential (mu). We…
We show that the effective potentials for the Polyakov loops in finite temperature SU$(N)$ gauge theories obey a certain scaling relation with respect to temperature in the large-$N$ limit. This scaling relation strongly constrains the…
We build a matrix model of a chiral [SU(N)]^K gauge theory (5D SQCD deconstructed down to 4D) using random unitary matrices to model chiral bifundamental fields (N,N-bar) (without (N-bar,N)). We verify the duality by matching the loop…
We discuss a representation of the Z(3) Gauge-Higgs lattice field theory at finite density in terms of dual variables, i.e., loops of flux and surfaces. In the dual representation the complex action problem of the conventional formulation…
The values of renormalized Polyakov loops in the three lowest representations of SU(3) were measured numerically on the lattice. We find that in magnitude, condensates respect the large-N property of factorization. In several ways, the…
We study a chiral N=1, U(N) field theory in the context of the Dijkgraaf-Vafa correspondence. Our model contains one adjoint, one conjugate symmetric and one antisymmetric chiral multiplet, as well as eight fundamentals. We compute the…
We calculate the deconfinement line of transitions for large Nc QCD at finite temperature and chemical potential in two different regimes: weak coupling in the continuum, and, strong coupling on the lattice, working in the limit where Nf is…
We calculate an effective Polyakov line action of QCD at large Nc and large Nf from a combined lattice strong coupling and hopping expansion working to second order in both, where the order is defined by the number of windings in the…
The well-known Yang-Mills theory with one $ S^{1} / Z_{2}$ universal extra dimension (UED) is generalized to an arbitrary number of spatial extra dimensions through a novel compactification scheme. In this paper, the Riemannian flat based…
The paper studies the convergence, as $N$ tends to infinity, of a system of $N$ coupled Hamilton-Jacobi equations, the Nash system. This system arises in differential game theory. We describe the limit problem in terms of the so-called…
Inspired by the formulation of the Batalin-Vilkovisky method of quantization in terms of ``odd time'', we show that for a class of gauge theories which are first order in the derivatives, the kinetic term is bilinear in the fields, and the…
Critical properties of the compact three-dimensional U(1) lattice gauge theory are explored at finite temperatures on an asymmetric lattice. For vanishing value of the spatial gauge coupling one obtains an effective two-dimensional spin…
We continue our analysis of establishing the reliability of "simple" effective theories where massive fields are "frozen" rather than integrated out, in a wide class of four dimensional theories with global or local N=1 supersymmetry. We…
Meson masses and decay constants in the large $N$ limit of SU($N$) gauge theory are determined using the twisted Eguchi-Kawai reduced model. To this end, we make use of a recently defined smearing method valid on the one-point lattice. This…
We had previously obtained an integral equation for mesons in transverse lattice QCD, in the limit of large number of colours and strong transverse lattice gauge coupling [1]. This equation is a generalisation of the 't Hooft equation [2],…
In this note we summarize the results from a longer article on obtaining the QCD phase diagram as a function of the temperature and chemical potential at large Nc and large Nf in the weak and the strong coupling limits. The weak coupling…