Related papers: Comments on the U(2) Noncommutative Instanton

We consider the action on instanton moduli spaces of the non-local symmetries of the self-dual Yang-Mills equations on $\mathbb{R}^4$ discovered by Chau and coauthors. Beginning with the ADHM construction, we show that a sub-algebra of the…

We study the noncommutative U(2) monopole solution at the second order in the noncommutativity parameter \theta^{ij}. We solve the BPS equation in noncommutative super Yang-Mills theory to O(\theta^2), transform the solution to the…

We give a mathematically rigorous proof of Nekrasov's conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on $\mathbb R^4$ gives a deformation of the Seiberg-Witten prepotential for N=2 SUSY…

We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R x G/H carries a G_2-structure. After imposing a general G-invariance condition,…

We construct static axially symmetric solutions of SU(2) Einstein-Yang-Mills-dilaton theory. Like their spherically symmetric counterparts, these solutions are nonsingular and asymptotically flat. The solutions are characterized by the…

In four dimensions, 't Hooft symbols offer a compact and powerful framework for describing the self-dual structures fundamental to instanton physics. Extending this to six dimensions, the six-dimensional 't Hooft symbols can be constructed…

These notes aim at a pedagogical introduction to recent work on deformation of spaces and deformation of vector bundles over them, which are relevant both in mathematics and in physics, notably monopole and instanton bundles. We first…

We construct new axially symmetric solutions of SU(2) Yang-Mills theory in a four dimensional anti-de Sitter spacetime. Possessing nonvanishing nonabelian charges, these regular configurations have also a nonzero angular momentum. Numerical…

We consider Lie(G)-valued G-invariant connections on bundles over spaces G/H, RxG/H and R^2xG/H, where G/H is a compact nearly Kaehler six-dimensional homogeneous space, and the manifolds RxG/H and R^2xG/H carry G_2- and Spin(7)-structures,…

We show that vortices of Yang-Mills-Higgs model in $R^{2}$ space can be regarded as instantons of Yang-Mills model in $R^{2}\times Z_{2}$ space. For this, we construct the noncommutative $Z_{2}$ space by explicitly fixing the $Z_{2}$…

We elaborate on the dynamics of noncommutative two-dimensional gauge field theories. We consider U(N) gauge theories with fermions in either the fundamental or the adjoint representation. Noncommutativity leads to a rather non-trivial…

The explicit multi-instanton solutions by 'tHooft and Jackiw, Nohl & Rebbi are generalized to curvilinear coordinates. The idea is that a gauge transformation can notably simplify the expressions obtained after the change of variables. The…

The series of perturbative fluctuations around a multi-instanton contribution to a specific class of correlation functions of supercurrents in $\cal N=4$ supersymmetric SU(N) Yang-Mills theory is examined in the light of the AdS/CFT…

The basic objects of the ADHM construction are reformulated in terms of elements of the $A_{\theta}(R^4)$ algebra of the noncommutative $R_{\theta}^4$ space. This new formulation of the ADHM construction makes possible the explicit calculus…

We construct U(2) BPS monopole superpartner solutions in N=2 non-commutative super Yang-Mills theory. Calculation to the second order in the noncommutative parameter $\theta$ shows that there is no electric quadrupole moment that is…

We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is the first in a series…

$U(n\otimes m)\ast$ gauge field theory on noncommutative spacetime is formulated and the standard-like model with the symmetry ${\text{U}(3_c\otimes 2\otimes 1_{\text{\scriptsize$Y$}})\ast}$ is reconstructed based on it. $\text{U}(n+m)\ast$…

Self-consistent Ansaetze are presented for the left- and right-handed isodoublet fermion zero-modes of the constrained instanton Istar in the vacuum sector of euclidean SU(2) Yang-Mills-Higgs theory. These left- and right-handed fermion…

We present a classification of SU(2) instantons on $T^2\times\mathbb{R}^2$ according to their asymptotic behaviour. We then study the existence of such instantons for different values of the asymptotic parameters, describing explicitly the…

A self-consistent non-minimal non-Abelian Einstein-Yang-Mills model, containing three phenomenological coupling constants, is formulated. The ansatz of a vanishing Yang-Mills induction is considered as a particular case of the self-duality…