Hyperbolic calorons, monopoles, and instantons

TL;DR

This paper constructs symmetric instantons and calorons in hyperbolic space, demonstrating their relationships with monopoles and Euclidean calorons as limits, thus advancing understanding of gauge configurations in curved spaces.

Contribution

It introduces a family of SO(3)-symmetric instantons and calorons on hyperbolic space, linking them to monopoles and Euclidean calorons as special cases.

Findings

Constructed SO(3)-symmetric charge 1 instantons and calorons on H^3 x R.

Demonstrated how calorons include instantons and hyperbolic monopoles as limits.

Showed Euclidean calorons as the flat space limit of hyperbolic calorons.

Abstract

We construct families of SO(3)-symmetric charge 1 instantons and calorons on the space H^3 x R. We show how the calorons include instantons and hyperbolic monopoles as limiting cases. We show how Euclidean calorons are the flat space limit of this family.