A Nahm transform for rotating calorons

TL;DR

This paper introduces a Nahm transform for rotating calorons, establishing a correspondence with solutions to a delayed-differential equation, and constructs a family of such calorons with specific properties.

Contribution

It formulates a novel Nahm transform for rotating calorons and proves the existence of a new family with nontrivial holonomy and rotational angle.

Findings

Proves existence of an eight-parameter family of charge 1 rotating calorons.

Constructs and visualizes these calorons using a numerical Nahm transform.

Establishes a link between rotating calorons and solutions of a delayed-differential equation.

Abstract

Rotating calorons were introduced in the context of rotating quark-gluon plasmas. They are anti-self-dual gauge fields on $\mathbb{R}^4$ that are invariant under a glide rotation. We formulate a Nahm transform which identifies rotating calorons with solutions of a delayed-differential equation. Using this transform, we prove existence of an eight-parameter family of charge 1 rotating calorons with nontrivial holonomy and rotational angle $\pi$, which we construct and visualise using a numerical implementation of the Nahm transform.