Instanton-Meron Hybrid in the Background of Gravitational Instantons

TL;DR

This paper introduces a new method to generate solutions to self-dual Yang-Mills equations in gravitational instanton backgrounds, revealing exotic instanton-meron hybrid configurations with unique topological and physical properties.

Contribution

A novel algorithm for constructing solutions to (anti) self-dual Yang-Mills equations in gravitational instanton backgrounds, demonstrating the existence of instanton-meron hybrid configurations.

Findings

Solutions are non-singular with finite Euclidean YM actions.

Configurations exhibit fractional topological charges.

Solutions resemble instantons more than merons in nature.

Abstract

When it comes to the topological aspects, gravity may have profound effects even at the level of particle physics despite its negligibly small relative strength well below the Planck scale. In spite of this intriguing possibility, relatively little attempt has been made toward the exhibition of this phenomenon in relevant physical systems. In the present work, perhaps the simplest and the most straightforward new algorithm for generating solutions to (anti) self-dual Yang-Mills (YM) equation in the typical gravitational instanton backgrounds is proposed and then applied to find the solutions practically in all the gravitational instantons known. Solutions thus obtained turn out to be some kind of instanton-meron hybrids possessing mixed features of both. Namely, they are rather exotic type of configurations obeying first order (anti) self-dual YM equation which are everywhere non-singular and have finite Euclidean YM actions on one hand while exhibiting meron-like large distance behavior and carrying generally fractional topological charge values on the other. Close inspection, however, reveals that the solutions are more like instantons rather than merons in their generic natures.