Finite action Yang-Mills solutions on the group manifold

Dereli, Tekin and Schray, Jörg and Tucker, Robin (1996) Finite action Yang-Mills solutions on the group manifold. Journal of Physics A: Mathematical and General, 29 (16). pp. 5001-5005. ISSN 0305-4470

Abstract

We demonstrate that the left (and right) invariant Maurer-Cartan forms for any semi-simple Lie group enable solutions of the Yang-Mills equations to be constructed on the group manifold equipped with the natural Cartan - Killing metric. For the unitary unimodular groups the Yang-Mills action integral is finite for such solutions. This is explicitly exhibited for the case of SU(3).