Related papers: Yang-Mills Connections On Orientable and Nonorient…

We discuss extension of soliton theory and integrable systems to noncommutative spaces, focusing on integrable aspects of noncommutative anti-self-dual Yang-Mills equations. We give wide class of exact solutions by solving a Riemann-Hilbert…

After a brief review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, we present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus in two…

We show that two-dimensional SO(N) and Sp(N) Yang-Mills theories without fermions can be interpreted as closed string theories. The terms in the 1/N expansion of the partition function on an orientable or nonorientable manifold M can be…

We consider the Abelian Yang-Mills-Higgs functional, in the non-self dual scaling, on a complex line bundle over a closed Riemannian manifold of dimension $n\geq 3$. This functional is the natural generalisation of the Ginzburg-Landau model…

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…

The geometry of submanifolds is intimately related to the theory of functions and vector bundles. It has been of fundamental importance to find out how those two objects interact in many geometric and physical problems. A typical example of…

We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group $G$ associated to outer automorphisms of $G$, and their corresponding defects. We show that the gauge theory partition function with defects can be…

We present a proof that quantum Yang-Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the…

We construct and study the Yang-Mills measure in two dimensions. According to the informal description given by the physicists, it is a probability measure on the space of connections modulo gauge transformations on a principal bundle with…

In this paper, we study the convergence of Yang-Mills-Higgs fields defined on fiber bundles over Riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the Riemann surface is allowed to vary. We…

As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these studies, they have found that inverse images of such maps…

In this work, we study topological properties of surface bundles, with an emphasis on surface bundles with a spin structure. We develop a criterion to decide whether a given manifold bundle has a spin structure and specialize it to surface…

This is an introduction to the geometry of compact Riemann surfaces, largely following the books Farkas-Kra, Fay, Mumford Tata lectures. 1) Defining Riemann surfaces with atlases of charts, and as locus of solutions of algebraic equations.…

We consider the problem of identifying a unitary Yang-Mills connection $\nabla$ on a Hermitian vector bundle from the Dirichlet-to-Neumann (DN) map of the connection Laplacian $\nabla^*\nabla$ over compact Riemannian manifolds with…

Let $G$ be a connected reductive complex affine algebraic group and $K\subset G$ a maximal compact subgroup. Let $M$ be a compact complex torus equipped with a flat K\"ahler structure and $(E_G ,\theta)$ a polystable Higgs $G$-bundle on…

We construct the most general reducible connection that satisfies the self-dual Yang-Mills equations on a simply connected, open subset of flat $\mathbb{R}^4$. We show how all such connections lie in the orbit of the flat connection on…

Moduli spaces of semi-stable real and quaternionic vector bundles of a fixed topological type admit a presentation as Lagrangian quotients, and can be embedded into the symplectic quotient corresponding to the moduli variety of semi-stable…

This supplementary manuscript is to describe an important nontrivial example, which appears in the matrix model of type IIB in the super string theory in order to apply a new duality for the moduli spaces of Yang-Mills connections on…

There are two notions of Yang-Mills action functional in noncommutative geometry. We show that for noncommutative n-torus both these notions agree. We also prove a structure theorem on the Hermitian structure of a finitely generated…

Recently, a non-hyperelliptic curve describing the Coulomb branch of N=2 SUSY $SU(N_c)$ Yang-Mills theory with an antisymmetric tensor matter was proposed using a configuration of a single M theory five-brane. We study the singular surface…