2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54712We study the non-abelian extension for the splitting of a scalar field into chiral components. Using this procedure we find a non ambiguous way of coupling a non abelian chiral scalar field to gravity. We start with a (non-chiral) WZW model covariantly coupled to a background metric and, after the splitting, arrive at two chiral Wess-Zumino-Witten (WZW) models coupled to gravity.10 pages, LATEXHigh Energy Physics - Theorytext