Drinfeld-Manin Instanton and Its Noncommutative Generalization

TL;DR

This paper reformulates the Drinfeld-Manin instanton construction within the ADHM framework, providing explicit solutions for U(N) instantons, and extends the approach to noncommutative spaces, offering systematic results for different N and k values.

Contribution

It introduces a reformulation of the Drinfeld-Manin instanton in the ADHM formalism and generalizes it to noncommutative geometry with explicit solutions.

Findings

Explicit solutions for U(N) instantons with N>=2k-1

Systematic constraints for N<2k-1 cases

Generalization to noncommutative spaces

Abstract

The Drinfeld-Manin construction of U(N) instanton is reformulated in the ADHM formulism, which gives explicit general solutions of the ADHM constraints for U(N) (N>=2k-1) k-instantons. For the N<2k-1 case, implicit results are given systematically as further constraints, which can be used to the collective coordinate integral. We find that this formulism can be easily generalized to the noncommutative case, where the explicit solutions are as well obtained.