Rigid string instantons are pseudo-holomorphic curves

TL;DR

This paper demonstrates that rigid string instantons in four-dimensional manifolds are pseudo-holomorphic curves in twistor space, providing explicit formulas for flat and spherical cases, and explores their implications for 4-manifold topology and Yang-Mills theory.

Contribution

It introduces explicit expressions for rigid string instantons as pseudo-holomorphic curves in twistor space for general 4-manifolds, with detailed formulas for R^4 and S^4.

Findings

Rigid string instantons are pseudo-holomorphic curves in twistor space.

Explicit formulas are provided for M=R^4 and S^4.

Potential connections to 4-manifold topology and Yang-Mills fields are discussed.

Abstract

We show how to find explicit expressions for rigid string instantons for general 4-manifold $M$. It appears that they are pseudo-holomorphic curves in the twistor space of $M$. We present explicit formulae for $M=R^4, S^4$. We discuss their properties and speculate on relations to topology of 4-manifolds and the theory of Yang-Mills fields.