On Yang-Mills fields from anti-de Sitter spaces

TL;DR

This paper constructs classical Yang-Mills gauge fields in anti-de Sitter space using non-compact foliations and conformal mappings, extending previous work with SU(2) to SU(1,1), and analyzes their properties including divergences.

Contribution

It introduces a novel method to obtain Yang-Mills fields from non-compact foliations of AdS4 and explores their transfer to Minkowski space, including Abelian and non-Abelian cases.

Findings

Constructed gauge fields in AdS4 using non-compact foliations.

Transferred these fields to Minkowski spacetime via conformal maps.

Identified divergences at a hyperboloid in the conformal boundary, yet found physically relevant solutions in the Abelian case.

Abstract

Motivated by some recent progress involving a non-compact gauge group, we obtain classical gauge fields using non-compact foliations of anti-de Sitter space in 4 dimensions (required dimensionality for conformal invariance of Yang-Mills theory) and transfer these to Minkowski spacetime using a series of conformal maps. This construction also builds upon some previous works involving SU(2) gauge group in that we now use its non-compact counterpart SU(1, 1) here. We note down gauge fields in both Abelian as well as non-Abelian settings and find them to be divergent at some hyperboloid, which is a hypersurface of co-dimension 1 inside the conformal boundary of AdS4. In spite of this hurdle we find a physically relevant field configuration in the Abelian case, reproducing a known result.