Related papers: Fiber Bundles, Yang-Mills Theory, and General Rela…
We derive five-dimensional super Yang-Mills theory from mass-deformed ABJM theory by expanding about $S^2$ for large Chern-Simons level $K$. We obtain the Yang-Mills coupling constant $g_{YM}^2 = 4\pi^2 R/K$. If we consider $S^3/{\mb{Z}_K}$…
Electromagnetism can be generalized to Yang-Mills theory by replacing the group U(1)$ by a nonabelian Lie group. This raises the question of whether one can similarly generalize 2-form electromagnetism to a kind of "higher-dimensional…
We study a class of noncommutative geometries that give rise to dimensionally reduced Yang-Mills theories. The emerging geometries describe sets of copies of an even dimensional manifold. Similarities to the D-branes in string theory are…
Contribution to the Proceedings of the International Congress of Mathematicians 1994. We review recent developments in the physics and mathematics of Yang-Mills theory in two dimensional spacetimes. This is a condensed version of a…
The canonical formulation of general relativity is based on decomposition space--time manifold $M$ into $ R\times \Sigma$, this decomposition has to preserve the invariance of general relativity, invariance under general coordinates, and…
A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions,…
In earlier work we proposed a string theory dual to two dimensional Yang-Mills theory at zero coupling (which can also be thought of as a $BF$ theory), given by a Polyakov-like generalization of Ho\v rava's topological rigid string theory,…
This paper recalls the development of gauge theory culminating in Yang-Mills theory, and the application of differential geometry including connections on fiber bundles to field theory. Finally, we see how the preceding is used to explain…
A class of new nonabelian gauge theories for vector fields on three manifolds is presented. The theories describe a generalization of three-dimensional Yang-Mills theory featuring a novel nonlinear gauge symmetry and field equations for…
Quantum Yang-Mills theory and the Wilson loop can be rewritten identically in terms of local gauge-invariant variables being directly related to the metric of the dual space. In this formulation, one reveals a hidden high local symmetry of…
In this Letter, we propose a model which is equivalent to the Yang-Mills theory at long distances but for which all symmetries are realized linearly. On top of the gauge and Fadeev-Popov ghosts fields, the model presents several massive…
I discuss the (2,2)-formalism of general relativity based on the (2,2)-fibration of a generic 4-dimensional spacetime of the Lorentzian signature. In this formalism general relativity is describable as a Yang-Mills gauge theory defined on…
We present a description of two dimensional Yang-Mills gauge theory on the plane and on compact surfaces, examining the topological, geometric and probabilistic aspects.
Lagrangian classical field theory of even and odd fields is adequately formulated in terms of fibre bundles and graded manifolds. In particular, conventional Yang-Mills gauge theory is theory of connections on smooth principal bundles, but…
There is a natural way to study the long distance interactions of gauge theories in the electric (momentum) representation. Here, the main ideas are presented for the Abelian and Yang-Mills gauge theories emphasizing on the structure and…
We make a short review of the formalism that describes Higgs and Yang Mills fields as two particular cases of an appropriate generalization of the notion of connection. We also comment about the several variants of this formalism, their…
We give a new description of classical Yang-Mills theory by coupling a two-dimensional chiral CFT (which gives the tree-level S-matrix of Yang-Mills theory at genus zero) to a background non-abelian gauge field. The resulting model is…
In this paper we consider the classification problem of extensions of Yang-Mills-type (YMT) theories. For us, a YMT theory differs from the classical Yang-Mills theories by allowing an arbitrary pairing on the curvature. The space of YMT…
We investigate relationship between a gauge theory on a principal bundle and that on its base space. In the case where the principal bundle is itself a group manifold, we also study relations of those gauge theories with a matrix model…
Gauge symmetric methods for data representation and analysis utilize tools from the differential geometry of vector bundles in order to achieve consistent data processing architectures with respect to local symmetry and equivariance. In…