Related papers: Gauge fields on coherent sheaves
We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus in the limit when the torus becomes small. The zero-modes of the fields then decouple from the non-zero modes and give rise to a…
The possible actions of symmetry groups on generalized Higgs fields coupled to an Einstein-Yang-Mills field are studied with differential geometrical techniques involving principal and associated bundles. A classification of conjugacy…
Let $G$ be a finite group and $\Y$ a $G$-gerbe over an orbifold $\B$. A disconnected orbifold $\hat{\Y}$ and a flat U(1)-gerbe $c$ on $\hat{\Y}$ is canonically constructed from $\Y$. Motivated by a proposal in physics, we study a…
We quantize the interaction of gravity with a Yang-Mills and Higgs field using canonical quantization. Similar to the approach in a previous paper we discard the Wheeler-DeWitt equation and express the Hamilton constraint by the evolution…
The canonical quantization is performed at a light-front surface for the SU(N) Yang-Mills theory. The Weyl gauge is imposed as a gauge condition. The suitable parameterization is chosen for the transverse gauge field components in order to…
Let $M$ be a smooth algebraic variety of dimension $2(p+q)$ with an algebraic symplectic form and a compatible deformation quantization $\mathcal{O}_h$ of the structure sheaf. Consider a smooth coisotropic subvariety $j: Y \to M$ of…
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…
We clarify the origin of magic angles in twisted multilayered graphene using Yang-Mills flows in two dimensions. We relate the effective Hamiltonian describing the electrons in the multilayered graphene to the ${\bar\partial}_{A}$ operator…
We reinterpret the Faddeev-Popov gauge-fixing procedure of Yang-Mills theories as the definition of a topological quantum field theory for gauge group elements depending on a background connection. This has the advantage of relating…
The purpose of this paper is to prove that if $Y$ is a compact manifold, if $Z$ is an Anosov vector field on $Y$, and if $F$ is a flat vector bundle, there is a corresponding canonical nonzero section $\tau_{\nu}\left(i_{Z}\right)$ of the…
Established fundamental physics can be described by fields, which are maps. The source of such a map is space-time, which can be curved due to gravity. The map itself needs to be curved in its gauge field part so as to describe interaction…
We consider Yang-Mills theory with a compact structure group $G$ on a Lorentzian 4-manifold $M={\mathbb R}\times\Sigma$ such that gauge transformations become identity on a submanifold $S$ of $\Sigma$ (framing over $S\subset\Sigma$). The…
We study the supergravity dual of four-dimensional ${\mathcal{N}=1}$ superconformal field theories arising from wrapping M5-branes on a K\"ahler two-cycle inside a Calabi-Yau threefold. We derive an effective three-dimensional theory living…
We twist the monopole equations of Seiberg and Witten and show how these equations are realized in topological Yang-Mills theory. A Floer derivative and a Morse functional are found and are used to construct a unitary transformation between…
Symmetric gauge fields and invariant metrics in homogeneous spaces are found. Their use for finding exact solutions of the Einstein-Yang-Mills (EYM) equations is discussed.
Classical vacuum - pure gauge - solutions of Euclidean two-dimensional SU(2) Yang-Mills theories are studied. Topologically non-trivial vacua are found in a class of gauge group elements isomorphic to $S_2$. These solutions are unexpectedly…
We compute the cohomological Hall algebra of zero-dimensional sheaves on an arbitrary smooth quasi-projective surface $S$ with pure cohomology, deriving an explicit presentation by generators and relations. When $S$ has trivial canonical…
In this article, we investigate Hecke modifications of vector bundles on a smooth projective curve $X$ defined over an arbitrary field. We obtain structural results that allow us to reduce the classification problem of Hecke modifications…
We describe two extensions of the notion of a self-dual connection in a vector bundle over a manifold M from dim M=4 to higher dimensions. The first extension, Omega-self-duality, is based on the existence of an appropriate 4-form Omega on…
We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the gauge where the field strength is diagonal. Twisted sectors originate, as in Matrix string theory, from permutations of the eigenvalues around homotopically…