The ADHM Construction of Instantons on Noncommutative Spaces

Abstract

We present an account of the ADHM construction of instantons on Euclidean space-time ${\mathbb{R}}^4$ from the point of view of noncommutative geometry. We recall the main ingredients of the classical construction in a coordinate algebra format, which we then deform using a cocycle twisting procedure to obtain a method for constructing families of instantons on noncommutative space-time, parameterised by solutions to an appropriate set of ADHM equations. We illustrate the noncommutative construction in two special cases: the Moyal-Groenewold plane ${\mathbb{R}}_{\hslash }^4$ and the Connes-Landi plane ${\mathbb{R}}_{\theta }^4$.

Latex, 40 pages

References in corpus (2)

• Quantisation of twistor theory by cocycle twist
• Bäcklund Transformations for Noncommutative Anti-Self-Dual Yang-Mills Equations