Related papers: Yang-Mills moduli spaces over an orientable closed…

Considering $B$-branes over a complex manifold $X$ as objects of the bounded derived category of coherent sheaves over $X$, we define holomorphic gauge fields on $B$-branes and introduce the Yang-Mills functional for these fields. These…

We prove an $L^{2}$ energy gap result for Yang-Mills connections on principal $G$-bundles over compact K\"{a}hler surfaces with positive scalar curvature. We prove related results for compact simply-connected Calabi-Yau $2$-folds.

In the following article we study the limiting properties of the Yang-Mills flow associated to a holomorphic vector bundle E over an arbitrary compact K\"ahler manifold (X,{\omega}). In particular we show that the flow is determined at…

We apply numerical and analytic techniques to the study of Yang-Mills integrals with orthogonal, symplectic and exceptional gauge symmetries. The main focus is on the supersymmetric integrals, which correspond essentially to the bulk part…

Consider a vector bundle over a K\"ahler manifold which admits a Hermitian Yang-Mills connection. We show that the pullback bundle on the blowup of the K\"ahler manifold at a collection of points also admits a Hermitian Yang-Mills…

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$, and $\xi \colon P \to \Sigma$ a principal $G$-bundle. In earlier work we have shown that the moduli space $N(\xi)$ of central Yang- Mills connections, for…

It is demonstrated that there are smooth Yang-Mills potentials which correspond to monopoles and vortices of one-half winding number. They are the generic configurations, in contrast to the integral winding number configurations like the 't…

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…

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…

We have given a new description of the lattice Yang-Mills theory a la Cho-Faddeev-Niemi-Shabanov, which has enabled us to confirm in a gauge-independent manner "Abelian"-dominance and magnetic-monopole dominance in the Wilson loop average,…

Let $F: [0, \infty) \to [0, \infty)$ be a strictly increasing $C^2$ function with $F(0)=0$. We unify the concepts of $F$-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce…

In this paper we introduce a set of equations on a principal bundle over a compact complex manifold coupling a connection on the principal bundle, a section of an associated bundle with K\"ahler fibre, and a K\"ahler structure on the base.…

A new state-sum formula for the evaluation of the Yang-Mills measure in the Kauffman bracket skein algebra of a closed surface is derived. The formula extends the Kauffman bracket to diagrams that lie in surfaces other than the plane. It…

For an elliptic surface $q:Y \to \Sigma$, with prescribed singular fibres, Stefan Bauer proved directly via algebraic geometry that the stable bundles over $Y$, whose chern classes are pull backs from $\Sigma$, correspond to the stable…

We extend an $L^2$ energy gap result due independently to Min-Oo and Parker (1982) for Yang-Mills connections on principal $G$-bundles, $P$, over closed, connected, four-dimensional, oriented, smooth manifolds, $X$, from the case of…

We exhibit a transformation taking special Lagrangian submanifolds of a Calabi-Yau together with local systems to vector bundles over the mirror manifold with connections obeying deformed Hermitian-Yang-Mills equations. That is, the…

Let $A\neq 0$ be a complex number with $ |A|\neq 1$. Let $M$ be a compact smooth oriented $3$-manifold, the $SU(3)$-skein space of $M$, $S_A(M)$, is the vector space over $\mathbb{C}$ generated by framed oriented links (including framed…

We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to…

Phenomenological compactifications of M-theory involve 7-manifolds with G_2 holonomy and various singularities. Here we study local geometries with such singularities, by thinking of them as compactifications of 7d supersymmetric Yang-Mills…

We compute the homotopy type of the moduli space of flat, unitary connections over aspherical surfaces, after stabilizing with respect to the rank of the underlying bundle. Over the orientable surface M^g, we show that this space has the…