Yang-Mills instantons and dyons on homogeneous G_2-manifolds

TL;DR

This paper studies G-invariant Yang-Mills fields on specific G_2-structured manifolds, reducing the problem to particle mechanics and finding instanton, dyon, and periodic solutions through analytical and numerical methods.

Contribution

It introduces a reduction of Yang-Mills theory with torsion on R x G/H to Newtonian mechanics and constructs explicit instanton and dyon solutions on these manifolds.

Findings

Critical points analyzed for different cosets.

Analytical and numerical kink- and bounce-type solutions found.

Periodic solutions on S^1 x G/H and dyons on iR x G/H constructed.

Abstract

We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R x G/H carries a G_2-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on R x G/H is reduced to Newtonian mechanics of a particle moving in R^6, R^4 or R^2 under the influence of an inverted double-well-type potential for the cases G/H = SU(3)/U(1)xU(1), Sp(2)/Sp(1)xU(1) or G_2/SU(3), respectively. We analyze all critical points and present analytical and numerical kink- and bounce-type solutions, which yield G-invariant instanton configurations on those cosets. Periodic solutions on S^1 x G/H and dyons on iR x G/H are also given.