Related papers: Instantons on Calabi-Yau cones

We consider the Yang-Mills instanton equations on the four-dimensional manifold S^2xSigma, where Sigma is a compact Riemann surface of genus g>1 or its covering space H^2=SU(1,1)/U(1). Introducing a natural ansatz for the gauge potential,…

We study the Yang-Mills flow on a holomorphic vector bundle E over a compact Kahler manifold X . Along a solution of the flow, we show the curvature $i\Lambda F(A_t)$ approaches in $L^2$ an endomorphism with constant eigenvalues given by…

Recently, an exact description of instanton corrections to the moduli spaces of 4d N=2 supersymmetric gauge theories compactified on a circle and Calabi-Yau compactifications of Type II superstring theories was found. The equations…

In this note we introduce a Yang-Mills bar equation on complex vector bundles over compact Hermitian manifolds as the Euler-Lagrange equation for a Yang-Mills bar functional. We show the existence of a non-trivial solution of this equation…

Let $X$ be a compact, K\"ahler, Calabi-Yau threefold and suppose $X\mapsto \underline{X}\leadsto X_t$ , for $t\in \Delta$, is a conifold transition obtained by contracting finitely many disjoint $(-1,-1)$ curves in $X$ and then smoothing…

In this paper we explore contributions to non-perturbative superpotentials arising from instantons wrapping effective divisors in smooth Calabi-Yau four-folds. We concentrate on the case of manifolds constructed as complete intersections in…

We study the deformation theory of the Einstein-Yang-Mills system on a principal bundle with a compact structure group over a compact manifold. We first construct, as an application of the general slice theorem of Diez and Rudolph, a smooth…

We address the issue why Calabi-Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6) requires us to consider the vector spaces of two-forms and four-forms on an equal…

We present some results on instanton corrections to the hypermultiplet moduli space in Calabi-Yau compactifications of Type II string theories. Previously, using twistor methods, only a class of D-instantons (D2-instantons wrapping…

We construct examples of deformed Hermitian Yang-Mills connections and deformed Spin(7)-instantons (also called Spin(7) deformed Donaldson-Thomas connections) on the cotangent bundle of $\mathbb{C}\mathbb{P}^2$ endowed with the Calabi…

This partially expository paper provides a view of Yang-Mills equations from the perspective of complex variables, operator theory, and $C^{*}$-algebras. Through operator-valued pluriharmonic and skew-Hermitian differential forms, it…

We establish the general formalism for constructing metrics of Calabi-Yau (p+1)-folds in terms of that of a p-fold by adding a complex-line bundle. We present a few explicit low-lying examples. We further consider holomorphic linearization…

We consider the dimensional reduction of supersymmetric Yang-Mills on a Calabi-Yau 3-fold. We show by construction how the resulting cohomological theory is related to the balanced field theory of the Kaehler Yang-Mills equations introduced…

We introduce the $J$-equation on holomorphic vector bundles over compact K\"ahler manifolds and investigate some fundamental properties as well as examples of solutions. In particular, we provide an algebraic condition called (asymptotic)…

We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its…

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.…

We present several results concerning non-commutative instantons and the Seiberg-Witten map. Using a simple ansatz we find a large new class of instanton solutions in arbitrary even dimensional non-commutative Yang-Mills theory. These…

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a…

In this paper, we study the non-Hermitian Yang-Mills (NHYM for short) bundles over compact K\"ahler manifolds. We show that the existence of harmonic metrics is equivalent to the semisimplicity of NHYM bundles, which confirms the Conjecture…

We study zero modes of N=1/2 supersymmetric Yang-Mills action in the background of instantons. In this background, because of a quartic antichiral fermionic term in the action, the fermionic solutions of the equations of motion are not in…