Related papers: $G_2$-instantons on noncompact $G_2$-manifolds: re…
Two-dimensional Abelian Higgs model is considered. It is shown that Higgs mechanism of the gauge bosons masses generating is broken in presence of instantons. It is supposed that discussion can be generalized into the standard model of…
We introduce a particular embedding of seven dimensional self-duality membrane equations in C^3\times R which breaks G_2 invariance down to SU(3). The world-volume membrane instantons define SU(3) special lagrangian submanifolds of C^3. We…
We study $H$-instanton bundles on the infinite family of smooth three-dimensional varieties $X_e=\mathbb{P}(\mathcal{O}_{\mathbb{P}^2} \oplus \mathcal{O}_{\mathbb{P}^2}(e))$, for $e \geq 0$. We provide two distinct monadic descriptions of…
We study a class of inhomogeneous and anisotropic $G_2$ string cosmological models. In the case of separable $G_2$ models we show that the governing equations reduce to a system of ordinary differential equations. We focus on a class of…
Let $G/H$ be a compact homogeneous space, and let $\hat{g}_0$ and $\hat{g}_1$ be $G$-invariant Riemannian metrics on $G/H$. We consider the problem of finding a $G$-invariant Einstein metric $g$ on the manifold $G/H\times [0,1]$ subject to…
We consider the low energy dynamics of charge two instantons on noncommutative $\mathbb{R}^{2}_{NC}\times\mathbb{R}^{2}_{NC}$ in U(2) 5-dimensional super-Yang-Mills, using the Manton approximation for slow-moving instantons to calculate the…
In this paper, we study non-Newtonian fluids in a class of unbounded domains with noncompact boundaries. With respect to the resulting mathematical problems, we establish the global existence of solutions with arbitrary large flux under…
In this expository review we discuss various aspects of gauge theory. While the focus is on mathematics, wherever possible we make contact with theoretical high energy physics. Particular emphasis is placed on instantons and monopoles,…
We are concerned with nonexistence results of nonnegative weak solutions for a class of quasilinear parabolic problems with a potential on complete noncompact Riemannian manifolds. In particular, we highlight the interplay between the…
We consider Yang-Mills theory on manifolds ${\mathbb R}\times X$ with a $d$-dimensional Riemannian manifold $X$ of special holonomy admitting gauge instanton equations. Instantons are considered as particle-like solutions in $d+1$…
There seems to be close relationship between the moduli space of vortices and the moduli space of instantons, which is not yet clearly understood from a standpoint of the field theory. We clarify the reasons why many similarities are found…
We identify an infinite class of unbounded potentials for which the Coleman instantons do not exist in D-dimensional spacetime. For such potentials, the decay of a false vacuum is described by the new instantons introduced in [5,6,4]. For…
Cohomogeneity one actions on irreducible Riemannian symmetric spaces of compact type are classified into three cases: Hermann actions, actions induced by the linear isotropy representation of a Riemannian symmetric space of rank 2, and…
We consider the gauge neutral matter in the low--energy effective action for string theory compactification on a \cym\ with $(2,2)$ world--sheet supersymmetry. At the classical level these states (the \sing's of $E_6$) correspond to the…
This is a review to classify all finite energy solutios of the two dimensional non-linear sigma model. These solutions could be important in understanding the vacuum structure of the non-linear sigma model.
This note revisits recent results regarding the geometry and moduli of solutions of the heterotic string on manifolds $Y$ with a $G_2$ structure. In particular, such heterotic $G_2$ systems can be rephrased in terms of a differential…
This paper studies the Poisson equation for the $G_2$-Laplacian on 3-forms on the 7-sphere that are invariant under a transitive group action. We establish the existence and uniqueness of $G$-invariant solutions for $G=SU(4),\: Spin(7),\:…
Quantum non-perturbative geometry of the universal hypermultiplet is investigated. We consider the simple case when the D-instantons, originating from the Calabi-Yau wrapped D2-branes, preserve a U(1)xU(1) symmetry of the universal…
In this Letter we discuss a natural general relativistic mechanism that causes inhomogeneities and hence generates matter perturbations in the early universe. We concentrate on spikes, both incomplete spikes and recurring spikes, that…
We investigate about the existence of static solitons solutions in the inverse G-L free energy in phase transitions of {\phi}4 theory. We calculate all the characteristics of these solitons , like localized structure, finite energy and mass…