Related papers: Comments on the Gribov Ambiguity
We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general…
We investigate gauge theories and matter contents in F-theory compactifications on families of genus-one fibered Calabi-Yau 4-folds lacking a global section. To construct families of genus-one fibered Calabi-Yau 4-folds that lack a global…
This is the first of two papers on the global topology of the space $\textrm{Sub}(G)$ of all closed subgroups of $G=\textrm{PSL}_2(\mathbb{R})$, equipped with the Chabauty topology. In this paper, we study the spaces of lattices and…
In this work, we present a brief but insightful overview of the gauge theories, which are defined on $ n $-dimensional lattices by using finite gauge groups, in order to show how they can be interpreted as a Hamiltonian system with…
We suggest a simple grand unified theory where the fifth dimensional coordinate is compactified on an $S^1/(Z_2 \times Z_2')$ orbifold. This model contains additional ${\bf 10 + \overline{10}}$, (${\bf 15 + \overline{15}}$) and two ${\bf…
The hidden sector of heterotic $M$-theory vacua whose gauge bundle contains an anomalous $U(1)$ factor is discussed in detail. The mathematical formalism for computing the inhomogeneous transformation of the dilaton and K\"ahler moduli…
Let $M$ be a closed, oriented, simply connected 6-manifold. After localization away from 2, we give a homotopy decomposition of $\Sigma M$ in terms of spheres, Moore spaces and other recognizable spaces. As applications we calculate…
The gravitational corrections to the gauge coupling constants of abelian and non-abelian gauge theories has been shown to diverge quadratically. Since this result will have interesting consequences, this has been analyzed by several authors…
We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with…
Let $M$ be a smooth manifold. We use Chern-Weil theory to study the characteristic classes of principal $G$-bundles built from continuous families of $\pi_{1}(M)$-representations, where $G$ is a compact Lie group. We then relate these…
It is shown that SU(N) gauge theory coupled to adjoint Higgs can be explicitly re-written in terms of SU(N) gauge invariant dynamical variables with local physical interactions. The resultant theory has a novel compact abelian $U(1)^{(N -…
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…
First, we review the basic mathematical structures and results concerning the gauge orbit space stratification. This includes general properties of the gauge group action, fibre bundle structures induced by this action, basic properties of…
We show that global properties of gauge groups can be understood as geometric properties in M-theory. Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with $A_{N-1}$ gauge algebra and different…
I point out two of the subtleties referred to in the title. The first is that gauge-invariant magnetic systems may realized under general circumstances, as suggested by a simple theorem. The second subtlety is that care is needed to…
We survey several mathematical developments in the holonomy approach to gauge theory. A cornerstone of this approach is the introduction of group structures on spaces of based loops on a smooth manifold, relying on certain homotopy…
The quantisation of gauge invariant systems usually proceeds through some gauge fixing procedure of one type or another. Typically for most cases, such gauge fixings are plagued by Gribov ambiguities, while it is only for an admissible…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
Reggeon unitarity and non-abelian gauge field copies are focussed on as two Gribov discoveries that, it is suggested, may ultimately be seen as the most significant and that could, in the far distant future, form the cornerstones of his…
For a principal $\rmSU(n)$-bundle over a compact manifold of dimension $2,3,4$, we determine the orbit types of the action of the gauge group on the space of connections modulo pointed local gauge transformations. We find that they are…