Related papers: Nahm Poles and 0-Instantons

We prove parabolic versions of several known gap theorems in classical Yang-Mills theory. On an $\mathrm{SU}(r)$-bundle of charge $\kappa$ over the 4-sphere, we show that the space of all connections with Yang-Mills energy less than $4…

We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of $\Rb^n$. They arise naturally from basic considerations of noncommutative differential topology and have non-trivial global…

We study the non-commutative instanton solution proposed in hep-th/0009142 and obtain the spectrum of small oscillations. The spectrum thus obtained is in exact agreement with the spectrum of stringy excitations in a configuration of point…

For a smooth bounded domain $G\subset\mathbb{R}^3$ we consider maps $n\colon\mathbb R^3\setminus G\to\mathbb S^2$ minimizing the energy $E(n)=\int_{\mathbb R^3\setminus G}|\nabla n|^2 +F_s(n_{\lfloor\partial G})$ among $\mathbb S^2$-valued…

We study homogeneous instantons on the seven dimensional Stiefel manifold V in the context of $G_2$ and Sasakian geometry. According to the reductive decomposition of V we provide an explicit description of all invariant $G_2$ and Sasakian…

We find necessary and sufficient conditions for a Riemannian four-dimensional manifold $(M, g)$ with anti-self-dual Weyl tensor to be locally conformal to a Ricci--flat manifold. These conditions are expressed as the vanishing of scalar and…

The scattering amplitudes of planar N = 4 super-Yang-Mills exhibit a number of remarkable analytic structures, including dual conformal symmetry and logarithmic singularities of integrands. The amplituhedron is a geometric construction of…

In this paper, we study the coupled Einstein constraint equations on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. This is physically well-motivated by standard cosmological…

Inspired by Lin-Pan-Wang (Comm. Pure Appl. Math., 65(6): 833-888, 2012), we continue to study the corresponding time-independent case of the Keller-Rubinstein-Sternberg problem. To be precise, we explore the asymptotic behavior of…

We study gauge-invariant approximations to the Yang-Mills vacuum wave functional in which asymptotic freedom and a detailed description of the infrared dynamics are encoded through squeezed core states. After variationally optimizing these…

Explicit construction of the basic SU(2) anti-instantons over the multi-Taub--NUT geometry via the classical conformal rescaling method is exhibited. These anti-instantons satisfiy the so-called weak holonomy condition at infinity with…

We present an expression for the leading-color (planar) four-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4-2 e dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity…

We study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in gradients of the hydrodynamic variables. At zeroth order conformal symmetry implies a constraint on the equation of state, E=2/3 P,…

The planar scattering amplitudes of $\mathcal{N} = 4$ super-Yang--Mills theory display symmetries and structures which underlie their relatively simple analytic properties such as having only logarithmic singularities and no poles at…

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…

We consider the Hermitian Yang-Mills (instanton) equations for connections on vector bundles over a 2n-dimensional K\"ahler manifold X which is a product Y x Z of p- and q-dimensional Riemannian manifold Y and Z with p+q=2n. We show that in…

We consider Ward's generalized self-duality equations for U(2r) Yang-Mills theory on R^{4k} and their Moyal deformation under self-dual noncommutativity. Employing an extended ADHM construction we find two kinds of explicit solutions, which…

We generalize the spectral-curve construction of moduli spaces of instantons on $\MT{4}$ and $K_3$ to noncommutative geometry. We argue that the spectral-curves should be constructed inside a twisted $\MT{4}$ or $K_3$ that is an elliptic…

We study the asymptotic behaviour of the solutions of the generic ($D_6^{(1)}$-type) third Painlev\'e equation in the space of initial values as the independent variable approaches infinity (or zero) and show that the limit set of each…

We prove sharp blow up rates of solutions of higher order conformally invariant equations in a bounded domain with an isolated singularity, and show the asymptotic radial symmetry of the solutions near the singularity. This is an extension…