Yang-Mills instantons on 7-dimensional manifold of G_2 holonomy

TL;DR

This paper explores Yang-Mills instantons on 7-dimensional G_2 holonomy manifolds, deriving reduced equations via symmetry assumptions and providing explicit and numerical solutions.

Contribution

It introduces a spherically symmetric ansatz for Yang-Mills connections on G_2 manifolds, leading to new reduced equations and solutions.

Findings

Derived explicit solutions for the instanton equations.

Obtained numerical solutions illustrating instanton behavior.

Reduced complex equations to manageable ordinary differential equations.

Abstract

We investigate Yang-Mills instantons on a 7-dimensional manifold of G_2 holonomy. By proposing a spherically symmetric ansatz for the Yang-Mills connection, we have ordinary differential equations as the reduced instanton equation, and give some explicit and numerical solutions.