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The non-abelian generalization of the Holdom model --{\it i.e.} a theory with two gauge fields coupled to the kinetic mixing term $g {tr}(F_{\mu \nu} (A) F_{\mu \nu} (B))$-- is considered. Contrarily to the abelian case, the group structure…
We define supersymmetric Yang-Mills theory on an arbitrary two-dimensional lattice (polygon decomposition) with preserving one supercharge. When a smooth Riemann surface $\Sigma_g$ with genus $g$ emerges as an appropriate continuum limit of…
Non-commutative differential geometry allows a scalar field to be regarded as a gauge connection, albeit on a discrete space. We explain how the underlying gauge principle corresponds to the independence of physics on the choice of vacuum…
Following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin (BFT), we embed the second-class non-abelian SU(2) Higgs model in the unitary gauge into a gauge invariant theory. The strongly involutive…
A gauge theory with an underlying SU_q(2) quantum group symmetry is introduced, and its properties examined. With suitable assumptions, this model is found to have many similarities with the usual SU(2)\times U(1) Standard Model,…
We consider a non-anticommutative N=2 superspace with an SU(2) singlet and Lorentz scalar deformation parameter, $\{\theta^{\alpha i},\theta^{\beta j}\}_\star = -2iP \e^{\alpha\beta}\e^{ij}$. We exploit this unique feature of the N=2 case…
We discuss the perturbative expansion of SU(N) Yang-Mills theories defined on a d-dimensional torus of linear size l with twisted boundary conditions, generalizing previous results in the literature. For a specific class of twist tensors…
In the standard formulation of relativistic quantum field theory, a $\mathbb{Z}_2$-graded structure is assumed to realize locality and the boson-fermion dichotomy. While $\mathbb{Z}_2^n$-graded extensions are known to be allowed at the…
We examine the restoration of the residual gauge symmetry in the Yang-Mills theory to be regarded as a confinement criterion. For this purpose we restrict the four-dimensional $SU(2)$ Yang-Mills instantons to those with spatial spherical…
This thesis addresses two topics: noncommutative Yang-Mills theories and the AdS/CFT correspondence. In the first part we study a partial summation of the theta-expanded perturbation theory. The latter allows one to define noncommutative…
Using a regularisation of the chiral SU(2) Yang-Mills model by an infinite number of Pauli-Villars fields the doubler free gauge invariant lattice model is constructed. Its continuum limit provides the recently proposed mechanism for…
We consider SU(2)-equivariant dimensional reduction of Yang-Mills-Dirac theory on manifolds of the form M x CP(1), with emphasis on the effects of non-trivial magnetic flux on CP(1). The reduction of Yang-Mills fields gives a chain of…
Using superspace techniques, the complete and most general action of D=10 super-Yang--Mills theory is constructed at the alpha'^2 level. No other approximations, e.g., keeping only a subset of the allowed derivative terms, are used. The…
A new set of tetrads is introduced within the framework of SU(2) X U(1) Yang-Mills field theories in four dimensional Lorentz curved spacetimes. Each one of these tetrads diagonalizes separately and explicitly each term of the Yang-Mills…
SU(2) Yang-Mills Theory coupled to massive adjoint scalar matter is studied in (1+1) dimensions using Discretised Light-Cone Quantisation. This theory can be obtained from pure Yang-Mills in 2+1 dimensions via dimensional reduction. On the…
We prove the perturbative renormalisability of pure SU(2) Yang-Mills theory in the abelian gauge supplemented with mass terms. Whereas mass terms for the gauge fields charged under the diagonal U(1) allow to preserve the standard form of…
We study dimensional reductions of noncommutative electrodynamics on flat space which lead to gauge theories of gravitation. For a general class of such reductions, we show that the noncommutative gauge fields naturally yield a Weitzenbock…
We study the volume dependence of electric flux energies for SU(2) gauge theory with twisted boundary conditions. The curves interpolate smoothly between the perturbative semiclassicalresults and the Confinement regime. On the basis of our…
The relationship between gauge and gravity amounts to understanding underlying new geometrical local structures. These structures are new tetrads specially devised for Yang-Mills theories, Abelian and Non-Abelian in four-dimensional…
A new local gauge invariant method is introduced in order to maximally simplify the expression for a SU(2) non-Abelian field strength. The new tetrads introduced in previous works are going to play a fundamental role in the algorithm…