Related papers: Comments on the U(2) Noncommutative Instanton
Given a bundle gerbe with connection on an oriented Riemannian manifold of dimension at least equal to 3, we formulate and study the associated Yang-Mills equations. When the Riemannian manifold is compact and oriented, we prove the…
The SU(4)-instanton equations are natural BPS equations for instantons on 8-manifolds. We study these equations on nearly Kaehler and Calabi-Yau torsion manifolds of the form M x G/H, with G/H a coset space and M a product of a torus with…
We show that the moduli space of the $(2,0)$ and little-string theories compactified on $T^3$ with R-symmetry twists is equal to the moduli space of U(1) instantons on a non-commutative $T^4$. The moduli space of $U(q)$ instantons on a…
Instanton calculations are demonstrated from a viewpoint of twisted topological field theory. Various properties become manifest such that perturbative corrections are terminated at one-loop, and norm cancellations occur between bosonic and…
The non-perturbative behavior of the N=2 supersymmetric Yang-Mills theories is both highly non-trivial and tractable. In the last three years the valuable progress was achieved in the instanton counting, the direct evaluation of the…
We construct static axially symmetric solutions of SU(2) Einstein-Yang-Mills-Higgs theory in the topologically trivial sector, representing gravitating monopole--antimonopole pairs, linked to the Bartnik-McKinnon solutions.
The $SO(4)\times U(1)$ Higgs model on $\R_4$ is extended by a $F^3$ term so that the action receives a nonvanishing contribution from the interactions of 2-instantons and 3-instantons, and can be expressed as the inverse of the Laplacian on…
The four-dimensional topological Yang-Mills theory with two anticommuting charges is naturally formulated on K\"ahler manifolds. By using a superspace approach we clarify the structure of the Faddeev-Popov sector and determine the total…
We give model-independent arguments, valid in nearly any number of spacetime dimensions, that topological solitons and instantons satisfy Bogomol'nyi-type bounds and, when these bounds are saturated, satisfy self-duality equations. In the…
We propose a systematic way of finding solutions to classical Yang-Mills equation with nontrivial topology. This approach is based on one of Wightman axioms for quantum field theory, which is referred to as form invariance condition in this…
We study the 1/4 BPS equations in the eight dimensional noncommutative Yang-Mills theory found by Bak, Lee and Park. We explicitly construct some solutions of the 1/4 BPS equations using the noncommutative version of the ADHM-like…
We continue our study of the noncommutative algebraic and differential geometry of a particular class of deformations of toric varieties, focusing on aspects pertinent to the construction and enumeration of noncommutative instantons on…
We have recently introduced the notion of a q-quaternion bialgebra and shown its strict link with the SO_q(4)-covariant quantum Euclidean space R_q^4. Adopting the available differential geometric tools on the latter and the quaternion…
Using spinorial geometry techniques, we classify the supersymmetric solutions of euclidean ${\cal N}=4$ super Yang-Mills theory. These backgrounds represent generalizations of instantons with nontrivial scalar fields turned on, and satisfy…
We show that $(1+2)$ nonlinear Klein-Gordon equation with negative coupling admits an exact solution which appears to be the linear superposition of the plane wave and the nonsingular rational soliton. We show that the same approach allows…
We study one-instantons, that is anti-selfdual connections with instanton number 1, on the quantum projective plane with orientation which is reversed with respect to the usual one. The orientation is fixed by a suitable choice of a basis…
We construct instanton solutions on noncommutative Euclidean 4-space which are deformations of instanton solutions on commutative Euclidean 4-space. We show that the instanton numbers of these noncommutative instanton solutions coincide…
We consider a dimensional reduction of the (deformed) Hermitian Yang-Mills condition on $S^1$-invariant K\"ahler Einstein $6$-manifolds. This allows us to reformulate the (deformed) Hermitian Yang-Mills equations in terms of data on the…
We study analytic aspects of U(n) gauge theory over a toric noncommutative manifold $M_\theta$. We analyse moduli spaces of solutions to the self-dual Yang-Mills equations on U(2) vector bundles over four-manifolds $M_\theta$, showing that…
We use the recursive structure of the compactification of the instanton moduli space of N=2 Super Yang-Mills theory with gauge group SU(2), to construct, by inductive limit, a universal moduli space which includes all the multi-instanton…