Related papers: Noncommutative Instantons and Solitons
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,…
A formulation of $\mathcal{N} = 2$ supersymmetric Yang-Mills theory with a spacetime-dependent gauge coupling allows to study the breaking of conformal symmetry at the quantum level. The theory has an energy-momentum tensor that is only…
These lectures deal mainly with solitons in three-dimensional Moyal-deformed sigma models. The topics are: static and moving (multi-)solitons of the (integrable) Ward sigma model, with space-space and time-space noncommutativity, their…
We construct new exact BPS solitons in various noncommutative gauge theories by the ``gauge'' transformation of known BPS solitons. This ``gauge'' transformation introduced by Harvey, Kraus and Larsen adds localized solitons to the known…
We consider an eight-dimensional local octonionic theory with the seven-sphere playing the role of the gauge group. Duality conditions for two- and four-forms in eight dimensions are related. Dual fields--octonionic instantons--solve an 8D…
The coulomb branch of $N=4$ supersymmetric Yang-Mills gauge theories in $d=2+1$ is studied. A direct connection between gauge theories and monopole moduli spaces is presented. It is proposed that the hyper-K\"ahler metric of supersymmetric…
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…
Some time ago, Atiyah and Manton observed that computing the holonomy of Yang-Mills instantons yields good approximations to static Skyrmion solutions of the Skyrme model. This paper provides an extension and explanation of this result, by…
A recent progress in obtaining non-spherical and non-static solitons in the four-dimensional Einstein--Yang--Mills (EYM) theory is discussed, and a non-perturbative formulation of the stationary axisymmetric problem is attempted. First a 2D…
We construct a spherically symmetric noncommutative space in three dimensions by foliating the space with concentric fuzzy spheres. We show how to construct a gauge theory in this space and in particular we derive the noncommutative version…
In these lectures, which are written at an elementary and pedagogical level, we discuss general aspects of (single) instantons in SU(N_c) Yang-Mills theory, and then specialize to the case of N = 4 supersymmetry and the large N_c limit. We…
We systematically classify all possible Bogomol'nyi-Prasad-Sommerfield (BPS) equations in Euclidean dimension $d\leq8$. We discuss symmetries of BPS equations and their connection with the self-dual Yang-Mills equations. Also, we present a…
For three conspicuous gauge groups, namely, SU(2), SU(3) and SO(5), and at first order in the noncommutative parameter matrix h\theta^{\mu\nu}, we construct smooth monopole --and, some two-monopole-- fields that solve the noncommutative…
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 a variety of physical systems in which one has states that can be thought of as generalised instantons. These include Yang--Mills theories on manifolds with a torsion-free $G$-structure, analogous gravitational instantons and…
We investigate non-BPS exact solutions in ${\mathbb C}P^{N-1}$ sigma models on ${\mathbb R}^1 \times S^{1}$ with twisted boundary conditions, by using the Din-Zakrzewski projection method. We focus on the relation of the non-BPS solutions…
We give an explicit expression for classical 1/4-BPS fields in supersymmetric Yang-Mills theory on noncommutative tori. We use it to study quantum 1/4-BPS states. In particular we calculate the degeneracy of 1/4-BPS energy levels.
We review our recent work on the BPS magnetic monopoles and its relation to the electromagnetic duality in the N=4 supersymmetric Yang-Mills systems with an arbitrary gauge group. The gauge group can be maximally or partially broken. The…
We construct a two parameter family of collapsing solutions to the 4+1 Yang-Mills equations and derive the dynamical law of the collapse. Our arguments indicate that this family of solutions is stable. The latter fact is also supported by…
We investigate the low-energy dynamics of the BPS solitons of the noncommutative CP^1 model in 2+1 dimensions using the moduli space metric of the BPS solitons. We show that the dynamics of a single soliton coincides with that in the…