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Classically, the dual under the Seiberg-Witten map of noncommutative U(N), {\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a \theta-deformed nonlinear realisation of the {\cal…
We propose a new description of the SU(N) Yang-Mills theory on a lattice, which enables one to explain quark confinement based on the dual superconductivity picture in a gauge independent way. This is because we can define gauge-invariant…
In the context of a semiclassical approach where vectorial gauge fields can be considered as classical fields, we obtain exact static solutions of the SU(N) Yang-Mills equations in a $(n+1)$ dimensional curved space-time, for the cases $n =…
The spectrum of the lightest bound states in N=1 supersymmetric Yang-Mills theory with SU(2) gauge group, calculated on the lattice, is presented. The masses have first been extrapolated towards vanishing gluino mass and then to the…
We present a mathematically rigorous canonical quantization of Yang-Mills theory in 1+1 dimensions (YM$_{1+1}$) by operator-algebraic methods. The latter are based on Hamiltonian lattice gauge theory and multi-scale analysis via inductive…
We study the physics of the Seiberg-Witten and Argyres-Faraggi-Klemm-Lerche-Theisen-Yankielowicz solutions of $D=4$, $\mathcal{N}=2$ and $\mathcal{N}=1$ $SU(N)$ supersymmetric gauge theory. The $\mathcal{N}=1$ theory is confining and its…
We simulate a supersymmetric matrix model obtained from dimensional reduction of 4d SU(N) super Yang-Mills theory. The model is well defined for finite N and it is found that the large N limit obtained by keeping g^2 N fixed gives rise to…
We explore further the Hamiltonian formulation of Yang-Mills theory in 2+1 dimensions in terms of gauge-invariant matrix variables. Coupling to scalar matter fields is discussed in terms of gauge-invariant fields. We analyze how the…
We compute the equation of state in the confining phase of SU(N) Yang-Mills theories with N=2, 3, 4, 5 and 6 colors in 2+1 dimensions, via lattice simulations. At low enough temperatures, the results are accurately described by a gas of…
The symmetries of the N=4 SuperYang-Mills theory on the light-cone are discussed, solely in terms of its physical degrees of freedom. We derive explicit expressions for the generators of the PSU(2,2|4) superalgebra, both in the free theory,…
In oder to investigate quark confinement, we give a new reformulation of the $SU(N)$ Yang-Mills theory on a lattice and present the results of the numerical simulations of the $SU(3)$ Yang-Mills theory on a lattice. The numerical…
The analysis of (2+1)-dimensional Yang-Mills ($YM_{2+1})$ theory via the use of gauge-invariant matrix variables is reviewed. The vacuum wavefunction, string tension, the propagator mass for gluons, its relation to the magnetic mass for…
We study N=1 supersymmetric SU(N) Yang-Mills theory on the lattice at strong coupling. Our method is based on the hopping parameter expansion in terms of random walks, resummed for any value of the Wilson parameter r in the small hopping…
We generalize the (2+1)-dimensional Yang-Mills theory to an anisotropic form with two gauge coupling constants $e$ and $e^{\prime}$. In an axial gauge, a regularized version of the Hamiltonian of this gauge theory is…
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…
The new approach to quantum mechanical problems is proposed. Quantum states are represented in an algebraic program, by lists of variable length, while operators are well defined functions on these lists. Complete numerical solution of a…
I present a novel analytic framework for $SU(N)$ Yang-Mills theory in the four-dimensional continuum. Background and effective field theory techniques are used to include non-perturbative contributions from cubic and quartic interactions.…
We consider $SU(N)$ Yang-Mills theories in $(2n+1)$-dimensional Euclidean spacetime, where $N\geq n+1$, coupled to an even flavour number of Dirac fermions. After integration over the fermionic degrees of freedom the wave functional for the…
A composite non-abelian model $SU(N) \times SU(N)$ is proposed as possible extension of the Yang-Mills symmetry. We obtain the corresponding gauge symmetry of the model and the most general lagrangian invariant by $SU(N) \times SU(N)$. The…
We study the large N (planar) limit of pure SU(N) 2+1 dimensional Yang-Mills theory (YM_{2+1}) using a gauge-invariant matrix parameterization introduced by Karabali and Nair. This formulation crucially relies on the properties of local…