Moduli Spaces of Noncommutative Instantons: Gauging Away Noncommutative Parameters Simon Brain and Giovanni Landi

Moduli Spaces of Instantons on Noncommutative 4-Manifolds

Studied are moduli spaces of self dual or anti-self dual connections on noncommutative 4-manifolds, especially deformation quantization of compact spin Riemannian 4-manifolds and their isometry groups have 2-torus subgroup. Then such moduli spaces of irreducible modules associated with highestweights of compact connected semisimple Lie groups are smooth manifolds with dimension determined by th...

A noncommutative-geometric interpretation of the resolution of equivariant instanton moduli spaces

We generalize the recently proposed noncommutative ADHM construction to the case of Γ-equivariant instantons over R, with Γ a Kleinian group. We show that a certain form of the inhomogeneous ADHM equations describes instantons over a noncommutative deformation of the Kleinian orbifold C/Γ and we discuss the relation of this with Nakajima’s description of instantons over ALE spaces. In particula...

Examples of noncommutative instantons

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 decribe toric noncommutative manifolds (also known as isospectral deformations). These come from deforming the usual Riemannian geometry of a manifold along a tor...

D1D5 System and Noncommutative Geometry

Supergravity on AdS3×S×T has dual description as a conformal sigma-model with the target space the moduli space of instantons on the noncommutative torus. We derive the precise relation between the parameters of this noncommutative torus and the parameters of the near-horizon geometry. We show that the low energy dynamics of the system of D1D5 branes wrapped on the torus of finite size is descr...

An Introduction to Noncommutative Spaces and their Geometry