Spherically symmetric selfdual Yang-Mills instantons on curved backgrounds in all even dimensions

TL;DR

This paper constructs and analyzes various classes of selfdual Yang-Mills instantons in all even-dimensional curved backgrounds, including constant curvature spaces and black hole spacetimes, with solutions exhibiting finite action and no backreaction.

Contribution

It provides new explicit solutions and existence proofs for selfdual Yang-Mills instantons in all even dimensions on diverse curved backgrounds, including black holes and (A)dS spaces.

Findings

Explicit closed-form solutions in certain backgrounds

Numerical solutions with proven existence

Instantons have finite action and do not alter the background geometry

Abstract

We present several different classes of selfdual Yang-Mills instantons in all even d backgrounds with Euclidean signature. In d=4p+2 the only solutions we found are on constant curvature dS and AdS backgrounds, and are evaluated in closed form. In d=4p an interesting class of instantons are given on black hole backgrounds. One class of solutions are (Euclidean) time-independent and spherically symmetric in d-1 dimensions, and the other class are spherically symmetric in all d dimensions. Some of the solutions in the former class are evaluated numerically, all the rest being given in closed form. Analytic proofs of existence covering all numerically evaluated solutions are given. All instantons studied have finite action and vanishing energy momentum tensor and do not disturb the geometry.