Conformal Symmetry on the Instanton Moduli Space

TL;DR

This paper explores how conformal symmetry acts on the instanton moduli space using the ADHM construction, revealing that the algebra closes up to gauge transformations and offering a 5D interpretation of the single-instanton.

Contribution

It introduces a homogeneous coordinate viewpoint for spacetime and moduli space, extending previous work by showing the conformal algebra closure involves gauge transformations.

Findings

Conformal algebra closes up to gauge transformations.

Homogeneous coordinates facilitate the analysis of symmetry.

A 5D interpretation of the SU(2) single-instanton is proposed.

Abstract

The conformal symmetry on the instanton moduli space is discussed using the ADHM construction, where a viewpoint of "homogeneous coordinates" for both the spacetime and the moduli space turns out to be useful. It is shown that the conformal algebra closes only up to global gauge transformations, which generalizes the earlier discussion by Jackiw et al. An interesting 5-dimensional interpretation of the SU(2) single-instanton is also mentioned.