# Harmonic spinors from twistors and potential forms

## TL;DR

This paper explores the construction of symmetry and transformation operators for twistor and harmonic spinors using conformal Killing-Yano forms, extending to gauged cases and discussing solutions to Seiberg-Witten equations.

## Contribution

It introduces new operators relating twistors and harmonic spinors, generalizes these to gauged cases, and discusses algebraic conditions for Seiberg-Witten solutions.

## Key findings

- Operators relating twistors to harmonic spinors are constructed.
- Gauged versions of these operators are developed.
- Conditions for solutions to Seiberg-Witten equations are analyzed.

## Abstract

Symmetry operators of twistor spinors and harmonic spinors can be constructed from conformal Killing-Yano forms. Transformation operators relating twistors to harmonic spinors are found in terms of potential forms. These constructions are generalized to gauged twistor spinors and gauged harmonic spinors. The operators that transform gauged twistor spinors to gauged harmonic spinors are found. Symmetry operators of gauged harmonic spinors in terms of conformal Killing-Yano forms are obtained. Algebraic conditions to obtain solutions of the Seiberg-Witten equations are discussed.