We study some topological aspects of non-abelian gauge theories intimately connected to the Lie algebras of the gauge groups and the homotopy theory in the generalized gauge orbit space. The physics connection to the non-perturbative solution to strong CP problem as originally proposed by the author is also discussed. Some relevant topological formulas are also given and discussed. A result fro...

Based on a generalization of the stochastic quantization scheme recently a modified FaddeevPopov path integral density for the quantization of Yang-Mills theory was derived, the modification consisting in the presence of specific finite contributions of the pure gauge degrees of freedom. Due to the Gribov problem the gauge fixing can be defined only locally and the whole space of gauge potentia...

We develop a general gauge invariant Lagrangian construction for half-integer higher spin fields in the AdS space of any dimension. Starting with formulation in terms of auxiliary Fock space we derive the closed nonlinear symmetry algebras of higher spin fermionic fields in the AdS space and find the corresponding BRST operator. A universal procedure of constructing the gauge invariant Lagrangi...

The aim of the present article is to give physical meaning to the ingredients of standard gauge field theory in the framework of the scale relativity theory. Owing to the principle of the relativity of scales, the scale-space is not absolute. Therefore, the scale variables are functions of the space-time coordinates, so that we expect a coupling between the displacement in space-time and the di...

We study the phase structure of four-dimensional N = 1 super Yang-Mills theories realized on D6-branes wrapping the RP of a Z2 orbifold of the deformed conifold. The non-trivial fundamental group of RP allows for the gauge group to be broken to various product groups by Z2 Wilson lines. We study the classical moduli space of theories in various pictures related by dualities including an M-theor...

Yang-Mills theories on a 1+1 dimensional cylinder are considered. It is shown that canonical quantization can proceed following different routes, leading to inequivalent quantizations. The problem of the non-free action of the gauge group on the configuration space is also discussed. In particular we re-examine the relationship between “θ-states” and the fundamental group of the configuration s...

We study exact effective superpotentials of four-dimensional N = 2 supersymmetric gauge theories with gauge group U(N) and various amounts of fundamental matter on R3 × S1, broken to N = 1 by turning on a classical superpotential for the adjoint scalar. On general grounds these superpotentials can easily be constructed once we identify a suitable set of coordinates on the moduli space of the ga...

Gravitational waves propagating through a stationary gauge field transform into gauge field waves and back again. When multiple families of flavor-space locked gauge fields are present, the gravitational and gauge field waves exhibit novel dynamics. At high frequencies, the system behaves like coupled oscillators in which the gravitational wave is the central pacemaker. Due to energy conservati...

Existence and uniqueness of the solution are proved for the ‘master equation’ derived from the BPS equation for the vector multiplet scalar in the U(1) gauge theory with NF charged matter hypermultiplets with eight supercharges. This proof finally establishes the fact that the moduli space of the BPS domain wall solution is CPNF−1 for the gauge theory at finite gauge couplings. Therefore the mo...

In the earlier works on quantum geometrodynamics in extended phase space it has been argued that a wave function of the Universe should satisfy a Schrödinger equation. Its form, as well as a measure in Schrödinger scalar product, depends on a gauge condition (a chosen reference frame). It is known that the geometry of an appropriate Hilbert space is determined by introducing the scalar product,...