Related papers: Quantum parameter space in super Yang-Mills, II
This paper aims to develop a non-commutative geometrical version of the theory of Yang--Mills--Scalar--Matter fields. To accomplish this purpose, we will dualize the geometrical formulation of this theory, in which principal $G$--bundles,…
We consider the order parameter $u=\left<{\rm Tr}\phi^2\right>$ as function of the running coupling constant $\tau \in \mathbb{H}$ of asymptotically free $\mathcal{N}=2$ QCD with gauge group $SU(2)$ and $N_f\leq 3$ massive hypermultiplets.…
Quantum matrix models in the large-N limit arise in many physical systems like Yang-Mills theory with or without supersymmetry, quantum gravity, string-bit models, various low energy effective models of string theory, M(atrix) theory,…
N=2 supersymmetric Yang-Mills theories are described in terms of a Hitchin system over a Riemann surface C. Focusing on strongly coupled Argyres-Douglas theories, we show that the corresponding flat bundle over C can be quantized such that…
The superspace flatness conditions which are equivalent to the field equations of supersymmetric Yang-Mills theory in ten dimensions have not been useful so far to derive non trivial classical solutions. Recently, modified flatness…
We perform the dual transformation of the Yang-Mills theory in d=3 dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but embedded into a flat…
Using noncommutative geometry we do U(1) gauge theory on the permutation group $S_3$. Unlike usual lattice gauge theories the use of a nonAbelian group here as spacetime corresponds to a background Riemannian curvature. In this background…
Supersymmetric gauge theories have had a significant impact on our understanding of QCD and of field theory in general. The phases of N=1 supersymmetric QCD (SQCD) are discussed, and the possibility of similar phases in non-supersymmetric…
In this research work the quantum theory of Ur-alternatives of Carl Friedrich von Weizs\"acker is considered. In This theory all objects and interactions in nature are constituted by abstract purely quantum logical relations in time. Such…
We present a first step towards generalizing the work of Seiberg and Witten on N=2 supersymmetric Yang-Mills theory to arbitrary gauge groups. Specifically, we propose a particular sequence of hyperelliptic genus $n-1$ Riemann surfaces to…
Supersymmetry is one of the possible scenarios for physics beyond the standard model. The building blocks of this scenario are supersymmetric gauge theories. In our work we study the $\mathcal{N}=1$ Super-Yang-Mills (SYM) theory with gauge…
A new non-perturbative approach to quantum field theory is proposed. Instead of performing a path integral over configurations of classical fields, D-theory works with discrete quantized variables. Classical spin fields are replaced by…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
Spherically and cylindrically symmetric solutions of SU(3) Yang-Mills theory are found, whose gauge potentials have confining properties. The spherically symmetric solutions give field distributions which have a spherical surface on which…
We study the gauge symmetry breaking of an ${\cal N}=1$ supersymmetric Yang-Mills theory defined on $M^4\times S^1$, taking correctly account of the vacuum expectation values for the adjoint scalar field $\vev{\Sigma}$ in vector multiplet…
We consider the pure supersymmetric Yang--Mills theories placed on a small 3-dimensional spatial torus with higher orthogonal and exceptional gauge groups. The problem of constructing the quantum vacuum states is reduced to a pure…
Non-Abelian strings for an Einstein-Yang-Mills-Higgs theory are explicitly constructed. We consider N_f Higgs fields in the fundamental representation of the U(1)xSU(N_c) gauge group in order to have a color-flavor SU(N_c) group remaining…
A new set of gauge invariant variables is defined to describe the physical Hilbert space of $d = 3 + 1$ $SU(2)$ Yang-Mills theory in the fixed-time canonical formalism. A natural geometric interpretation arises due to the $GL(3)$ covariance…
We analyze a recently proposed supersymmetry breaking mass deformation of the $E_1$ superconformal fixed point in five dimensions which, at weak gauge coupling, leads to pure $SU(2)$ Yang-Mills and which was conjectured to lead to an…
The relation between connections on 2-dimensional manifolds and holomorphic bundles provides a new perspective on the role of classical gauge fields in quantum field theory in two, three and four dimensions. In particular we show that there…