Harmonic Space, Self-Dual Yang Mills and the $N=2$ String

TL;DR

This paper explores the geometric and quantum aspects of a harmonic space formulation of self-dual Yang-Mills theory, revealing its relation to twistor geometry, its lack of quantum corrections, and clarifying its distinction from the N=2 string.

Contribution

It provides a detailed analysis of the harmonic space action for SDYM, clarifies its geometric structure, and demonstrates its trivial S matrix, differentiating it from the N=2 string.

Findings

The harmonic space formulation is closely related to twistor constructions.

The theory receives no quantum corrections.

Its S matrix is trivial, indicating it is not the N=2 string.

Abstract

The geometrical structure and the quantum properties of the recently proposed harmonic space action describing self-dual Yang-Mills (SDYM) theory are analyzed. The geometrical structure that is revealed is closely related to the twistor construction of instanton solutions. The theory gets no quantum corrections and, despite having SDYM as its classical equation of motion, its S matrix is trivial. It is therefore NOT the theory of the N=2 string. We also discuss the 5-dimensional actions that have been proposed for SDYM.