Symmetric calorons and the rotation map

Abstract

We study $SU(2)$ calorons, also known as periodic instantons, and consider invariance under isometries of $S^1\times {\mathbb{R}}^3$ coupled with a non-spatial isometry called the rotation map. In particular, we investigate the fixed points under various cyclic symmetry groups. Our approach utilises a construction akin to the ADHM construction of instantons -- what we call the monad matrix data for calorons -- derived from the work of Charbonneau and Hurtubise. To conclude, we present an example of how investigating these symmetry groups can help to construct new calorons by deriving Nahm data in the case of charge $2$.

26 pages

References in corpus (6)

• A survey on Nahm transform
• Chains of Skyrmions
• Large scale and large period limits of symmetric calorons
• Calorons, Nahm's equations on S^1 and bundles over P^1xP^1
• Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem
• Aspects of $C_3$-symmetric calorons from numerical Nahm transform

Cited by in corpus (6)

• Inhomogeneity of rotating gluon plasma and Tolman-Ehrenfest law in imaginary time: lattice results for fast imaginary rotation
• A model for gauged skyrmions with low binding energies
• Skyrmions from calorons
• Magnetically Charged Calorons with Non-Trivial Holonomy
• Symmetric calorons of higher charges and their large period limits
• Topology of Calorons Re-examined