New rigid string instantons in $R^4$

TL;DR

This paper introduces new rigid string instanton equations in four-dimensional space, revealing a novel splitting into three families and providing explicit solutions in certain cases.

Contribution

It derives and analyzes a new class of rigid string instanton equations that differ from standard cases by splitting into three families.

Findings

Equations split into three distinct families.

Explicit solutions are found in some cases.

The new equations expand understanding of string instantons in $R^4$.

Abstract

New rigid string instanton equations are derived. Contrary to standard case, the equations split into three families. Their solutions in $R^4$ are discussed and explicitly presented in some cases.