Doubly Periodic Instanton Zero Modes

TL;DR

This paper investigates fermionic zero modes in doubly periodic SU(2) instantons, revealing how their localization depends on boundary conditions and the instanton structure.

Contribution

It introduces the analysis of zero modes in doubly periodic instantons with complex core structures, highlighting the influence of boundary conditions on zero mode localization.

Findings

Zero modes peak on line segments connecting instanton constituents.

Boundary conditions determine which of the four possible zero mode localizations occurs.

Zero mode behavior depends on the instanton core configuration and boundary conditions.

Abstract

Fermionic zero modes associated with doubly periodic SU(2) instantons of unit charge are considered. In cases where the action density exhibits two `instanton cores' the zero mode peaks on one of four line-segments joining the two constituents. Which of the four possibilities is realised depends on the fermionic boundary conditions; doubly periodic, doubly anti-periodic or mixed.