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arXiv · 1008.4517

The ADHM Construction of Instantons on Noncommutative Spaces

Simon Brain·Walter D. van Suijlekom
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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 $\mathbb{R}^4_\hbar$ and the Connes-Landi plane $\mathbb{R}^4_\theta$.

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Simon Brain, Walter D. van Suijlekom. 2010-08-26. The ADHM Construction of Instantons on Noncommutative Spaces. https://doi.org/10.1142/s0129055x1100428x

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