Related papers: Loop Equation in Two-dimensional Noncommutative Ya…
In this paper, we review the construction and large $N$ study of the continuous two-dimensional Yang--Mills theory with gauge group $\mathrm{U}(N)$ through probability, combinatorics and representation theory. In the first part, we define…
The Makeenko-Migdal loop equation is non-linear and first order in the area derivative, but we show that for simple loops in QCD$_2$ it is possible to reformulate this equation as a linear equation with second order derivatives. This…
Quantum Yang-Mills theory and the Wilson loop can be rewritten identically in terms of local gauge-invariant variables being directly related to the metric of the dual space. In this formulation, one reveals a hidden high local symmetry of…
We present a powerful method to generate various equations which possess the Lax representations on noncommutative (1+1) and (1+2)-dimensional spaces. The generated equations contain noncommutative integrable equations obtained by using the…
We propose a formulation of d-dimensional SU(N) Yang-Mills theories on a d+2-dimensional space with the extra two dimensions forming a surface with non-commutative geometry. This equivalence is valid in any finite order in the 1/N…
We investigate Schwinger-Dyson equations for correlators of Wilson line operators in non-commutative gauge theories. We point out that, unlike what happens for closed Wilson loops, the joining term survives in the planar equations. This…
The large-N limit of the expectation values of the Wilson loops corresponding to two-dimensional U(N) Yang-Mills and generalized Yang-Mills theories on a sphere are studied. The behavior of the expectation values of the Wilson loops both…
These notes comprise the first of two articles devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. This first part deals solely with the classical theory on a noncommutative torus.…
It is known that noncommutative Yang-Mills theory with periodical boundary conditions on torus at the rational value of the noncommutativity parameter is Morita equivalent to the ordinary Yang-Mills theory with twisted boundary conditions…
We discuss extension of soliton theory and integrable systems to noncommutative spaces, focusing on integrable aspects of noncommutative anti-self-dual Yang-Mills equations. We give wide class of exact solutions by solving a Riemann-Hilbert…
We exhibit the gauge-group independence (``universality'') of all normalized non-intersecting Wilson loop expectation values in the large N limit of two-dimensional Yang-Mills theory. This universality is most easily understood via the…
The correspondence of the non-critical string theory and the Yang-Mills theory is examined according to the recent Polyakov's proposal, and two possible solutions of the bulk equations are addressed near the fixed points of the pure…
We derive an infinite sequence of Schwinger-Dyson equations for $N=1$ supersymmetric Yang-Mills theory. The fundamental and the only variable employed is the Wilson-loop geometrically represented in $N=1$ superspace: it organizes an…
We formulate noncommutative self-dual N=4 supersymmetric Yang-Mills theory in D=2+2 dimensions. As in the corresponding commutative case, this theory can serve as the possible master theory of all the noncommutative supersymmetric…
The large-N limit of the two-dimensional non-local U$(N)$ Yang-Mills theory on an orientable and non-orientable surface with boundaries is studied. For the case which the holonomies of the gauge group on the boundaries are near the…
We identify a universal finite-$N$ structure underlying Wilson loop expectations in lattice Yang-Mills, in any dimension $d\geq 2$, for gauge group $\mathrm{U}(N)$, and for arbitrary smooth central plaquette actions. The starting point is a…
We compute the Large N limit of several objects related to the two-dimensional Euclidean Yang-Mills measure on compact connected orientable surfaces of genus larger or equal to one, with a structure group taken among the classical groups of…
We study our Schwinger-Dyson equation as well as the large $N_{c}$ loop equation for supersymmetric Yang-Mills theory in four dimensions by the N=1 superspace Wilson-loop variable. We are successful in deriving a new manifestly…
We show that the noncommutative Yang-Mills field forms an irreducible representation of the (undeformed) Lie algebra of rigid translations, rotations and dilatations. The noncommutative Yang-Mills action is invariant under combined…
These notes, echoing a conference given at the Strasbourg-Zurich seminar in October 2017, are written to serve as an introduction to 2-dimensional quantum Yang-Mills theory and to the results obtained in the last five to ten years about its…