相关论文: Instantons on the Quantum 4-Spheres S^4_q

We introduce and analyse a new type of quantum 2-spheres. Then we apply index theory for noncommutative line bundles over these spheres to conclude that quantum lens spaces are non-crossed-product examples of principal extensions of…

The moduli space of k G-instantons on R^4 for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1)…

Some time ago, Atiyah showed that there exists a natural identification between the k-instantons of a Yang-Mills theory with gauge group $G$ and the holomorphic maps from $CP_1$ to $\Omega G$. Since then, Nair and Mazur, have associated the…

We study the U(1) and U(2) instanton solutions of gauge theory on general noncommutative $\bf{R}^4$. In all cases considered we obtain explicit results for the projection operators. In some cases we computed numerically the instanton charge…

The quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which…

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 show that noncommutative gauge theory in two dimensions is an exactly solvable model. A cohomological formulation of gauge theory defined on the noncommutative torus is used to show that its quantum partition function can be written as a…

We construct a model of spin-Hall effect on a noncommutative 4 sphere with isospin degrees of freedom (coming from a noncommutative instanton) and invariance under a quantum orthogonal group. The corresponding representation theory allows…

As part of our study of the $q$-tetrahedron algebra $\boxtimes_q$ we introduce the notion of a $q$-inverting pair. Roughly speaking, this is a pair of invertible semisimple linear transformations on a finite-dimensional vector space, each…

We define even dimensional quantum spheres Sigma_q^2n that generalize to higher dimension the standard quantum two-sphere of Podle's and the four-sphere Sigma_q^4 obtained in the quantization of the Hopf bundle. The construction relies on…

To some Hecke symmetries (i.e. Yang-Baxter braidings of Hecke type) we assign algebras called braided non-commutative spheres. For any such algebra, we introduce and compute a q-analog of the Chern-Connes index. Unlike the standard…

We study two classes of quantum spheres and hyperboloids which are $*$-quantum spaces for the quantum orthogonal group $\mathcal{O}(SO_q(3))$. We construct line bundles over the quantum homogeneous space of invariant elements for the…

In [20] Esnault asked whether on a general quotient surface singularity the rank and the first Chern class distinguish isomorphism classes of indecomposable reflexive modules. Wunram gave a contraexample in [46] showing two different full…

We present several different classes of selfdual Yang-Mills instantons in all even d backgrounds with Euclidean signature. In d=4p+2 the only solutions we found are on constant curvature dS and AdS backgrounds, and are evaluated in closed…

On an oriented, compact, connected, real four-dimensional manifold, $M$, we introduce a topological Lagrangian gauge field theory with a Bogomol'nyi structure that leads to non-singular, finite-Action, stable solutions to the variational…

The dimensional reduction of eleven dimensional supergravity on a Calabi-Yau manifold gives N=2 supergravity in five dimensions with $h_{1,1}$ vector and $h_{2,1}+1$ hypermultiplets. In this paper instanton solutions are constructed which…

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

The truncated 4-dimensional sphere $S^4$ and the action of the self-interacting scalar field on it are constructed. The path integral quantization is performed while simultaneously keeping the SO(5) symmetry and the finite number of degrees…

Motivated by Yang-Mills theory in 4n dimensions, and generalizing the notion due to Atiyah, Drinfeld, Hitchin and Manin for n=1, Okonek, Spindler and Trautmann introduced instanton bundles and special instanton bundles as certain algebraic…

This is a talk given on the $\theta $vacuum and cluster properties and the non-linear sigma model proposed to be given on occasion of an invitation to the seventh international conference on Symmetry in Nonlinear Physics,June 24 - 30, 2007,…