Biquaternion Construction of SL(2,C) Yang-Mills Instantons

TL;DR

This paper constructs SL(2,C) Yang-Mills instantons using biquaternions, revealing their moduli space and singularities, and extending previous solutions with new parameters and properties.

Contribution

It introduces a biquaternion-based method to construct SL(2,C) instantons, including new solutions with moduli parameters and inherent singularities.

Findings

Constructed SL(2,C) instantons with 16k-6 moduli parameters

Included previous (M,N) instanton solutions as a subset

Identified non-gauge artifact singularities in SL(2,C) instantons

Abstract

We use biquaternion to construct SL(2,C) ADHM Yang-Mills instantons. The solutions contain 16k-6 moduli parameters for the kth homotopy class, and include as a subset the SL(2,C) (M,N) instanton solutions constructed previously. In constrast to the SU(2) instantons, the SL(2,C) instantons inhereit jumping lines or singulariries which are not gauge artifacts and can not be gauged away.