We present a model for supersymmetric Yang-Mills theory in 10+2 dimensions. Our construction uses a constant null vector, and leads to a consistent set of field equations and constraints. The model is invariant under generalized translations and an extra gauge transformation. Ordinary dimensional reduction to ten dimensions yields the usual supersymmetric Yang-Mills equations, while dimensional...

Marchesini showed that the Fokker–Planck Hamiltonian for Yang-Mills theories is the loop operator. Jevicki and Rodrigues showed that the Fokker– Planck Hamiltonian of some matrix models cöıncides with temporal gauge non-critical string field theory Hamiltonians constructed by Ishibashi and Kawai (and their collaborators). Thus the loop operator for Yang–Mills theory is the temporal gauge Hamilt...

A exotic class of nonlinear p-form nonabelian gauge theories is studied, arising from the most general allowed nontrivial deformation of linear abelian gauge theory for a set of massless 1-form fields and 2-form fields in four dimensions. These theories combine a Chapline-Manton type coupling of the 1-forms and 2-forms, along with Yang-Mills coupling of the 1-forms, a Freedman-Townsend coupling...

Four dimensional Yang-Mills theory formulated through an action on twistor space has a larger gauge symmetry than the usual formulation, which in previous work was shown to allow a simple gauge transformation between text-book perturbation theory and the Cachazo-Svrček-Witten rules. In this paper we study non-supersymmetric twistor Yang-Mills theory at loop level using the background field meth...

We find solutions of the Yang-Mills field equations with gauge group SU(2) in 4k dimensions which have the interpretation of four-dimensional instantons at angles. These configurations satisfy a BPS-like condition which arises in the context of two-dimensional (4,0)-supersymmetric sigma models. Moreover we show that these solutions are examples of Hermitian-Einstein connections on E. In the pas...

In the context of D-dimensional Euclidean gravity, we define the natural generalisation to D-dimensions of the self-dual Yang-Mills equations, as duality conditions on the curvature 2-form of a Rie-mannian manifold. Solutions to these self-duality equations are provided by manifolds of SU (2), SU (3), G 2 and Spin(7) holonomy. The equations in eight dimensions are a master set for those in lowe...

We consider particle-like and black holes solutions of the Einstein-Yang-Mills system with positive cosmological constant in d > 4 spacetime dimensions. These configurations are spherically symmetric and present a cosmological horizon for a finite value of the radial coordinate, approaching asymptotically the de Sitter background. In the usual Yang–Mills case we find that the mass of these solu...

In the context of D-dimensional Euclidean gravity, we define the natural generalisation to D-dimensions of the self-dual Yang-Mills equations, as duality conditions on the curvature 2-form of a Rie-mannian manifold. Solutions to these self-duality equations are provided by manifolds of SU (2), SU (3), G 2 and Spin(7) holonomy. The equations in eight dimensions are a master set for those in lowe...

These notes give a pedagogical introduction to D-branes and Matrix theory. The development of the material is based on super Yang-Mills theory, which is the low-energy field theory describing multiple D-branes. The main goal of these notes is to describe physical properties of D-branes in the language of Yang-Mills theory, without recourse to string theory methods. This approach is motivated by...

In [7–9] and [10] the conjecture is presented that almost-commutative geometries, with respect to sensible physical constraints, allow only the standard model of particle physics and electro-strong models as Yang-Mills-Higgs theories. In this publication a counter example will be given. The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs model which consists of the standar...