Related papers: Frobenius Manifolds from Yang-Mills Instantons

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 prove that energy minimizing Yang-Mills connections on a compact $G_{2}$-manifold has holonomy equal to $G_{2}$ are $G_{2}$-instantons, subject to an extra condition on the curvature. Furthermore, we show that energy minimizing…

This is a survey of recent studies of singularity formation in solutions of spherically symmetric Yang-Mills equations in higher dimensions. The main attention is focused on five space dimensions because this case exhibits interesting…

We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural…

Recently, gauged supergravities in three dimensions with Yang-Mills and Chern-Simons type interactions have been constructed. In this article, we demonstrate that any gauging of Yang-Mills type with semisimple gauge group G_0, possibly…

We describe various approaches that give matrix descriptions of compactified NS five-branes. As a result, we obtain matrix models for Yang-Mills theories with sixteen supersymmetries in dimensions $2,3,4$ and 5. The equivalence of the…

The arcane ADHM construction of Yang-Mills instantons can be very naturally understood in the framework of D-brane dynamics in string theory. In this point-of-view, the mysterious auxiliary symmetry of the ADHM construction arises as a…

Starting from our proposed model of the Yang-Mills vacuum based on fractional instantons, we review the intellectual itinerary which has guided part of our scientific activity up to our recent work on adjoint zero-modes for calorons.

In this article we review, for a mathematical audience, the computation of (tree-level) scattering amplitudes in Yang-Mills theory in detail, in order to bridge the gap in understanding of the subject between mathematicians and physicists.…

The main goal of this paper is to introduce the notion of a primitive form for a generic family of Hurwitz covers of $\mathbb{P}^1$ with a fixed ramification profile over infinity. We prove that primitive forms are in one-to-one…

I explain how to construct noncommutative BPS configurations in four and lower dimensions by solving linear matrix equations. Examples are instantons in D=4 Yang-Mills, monopoles in D=3 Yang-Mills-Higgs, and (moving) solitons in D=2+1…

In recent years it has been shown that many, and possibly all, integrable systems can be obtained by dimensional reduction of self-dual Yang-Mills. I show how the integrable systems obtained this way naturally inherit bihamiltonian…

We construct a supersymmetric version of instanton operators in five-dimensional Yang-Mills theories. This is possible by considering a five-dimensional generalization of the familiar four-dimensional topologically twisted theory, where the…

We use biquaternion to construct SL(2,C) ADHM Yang-Mills instantons. The solutions contain 16k-6 moduli parameters for the kth homotopy class, and include as a subset the SL(2,C) (M,N) instanton solutions constructed previously. In…

In this review we present the octonionic duality for membranes. We start with a discussion on the relation of the Yang Mills theories and the supermembrane Hamiltonian in the light-cone gauge. We further derive the self-duality equations…

We study integrality of instanton numbers (genus zero Gopakumar - Vafa invariants) for quintic and other Calabi-Yau manifolds. We start with the analysis of the case when the moduli space of complex structures is one-dimensional; later we…

We show that twisted reduced models can be interpreted as noncommutative Yang-Mills theory. Based upon this correspondence, we obtain noncommutative Yang-Mills theory with D-brane backgrounds in IIB matrix model. We propose that IIB matrix…

A geometrization of the Yang-Mills field, by which an SU(2) gauge theory becomes equivalent to a 3-space geometry - or optical system - is examined. In a first step, ambient space remains Euclidean and current problems on flat space can be…

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the…

We extend previous work by developing a worldsheet description of non-abelian gauge theory (Yang-Mills). This task requires the introduction of Grassmann variables on the world sheet analogous to those of the Neveu-Schwarz-Ramond…