A Classical Solution in Six-dimensional Gauge Theory with Higher Derivative Coupling

TL;DR

This paper presents an exact solution to a six-dimensional SO(6) gauge theory with higher-derivative coupling, using the spin connection on a 6-sphere, and explores its topological properties.

Contribution

It introduces a novel exact solution to a generalized self-dual equation in six-dimensional gauge theory with higher derivatives, linked to the geometry of a 6-sphere.

Findings

Exact solution using spin connection on S^6

Topological charge proportional to winding number

Higher derivative coupling constant related to sphere radius

Abstract

We show that the spin connection of the standard metric on a six-dimensional sphere gives an exact solution to the generalized self-dual equations suggested by Tchrakian some years ago. We work on an SO(6) gauge theory with a higher-derivative coupling term. The model consists of vector fields only. The pseudo-energy is bound from below by a topological charge which is proportional to the winding number of spatial S^5 around the internal space SO(6). The fifth homotopy group of SO(6) is, indeed, Z. The coupling constant of higher derivative term is quadratic in the radius of the underlying space S^6.