General Leznov-Savelev solutions for Pohlmeyer reduced AdS5 minimal surfaces

Abstract

We consider the Pohlmeyer reduced sigma model describing AdS5 minimal surfaces. We show that, similar to the affine Toda models, there exists a conformal extension to this model which admits a Lax formulation. The Lax connection is shown to be valued in a \( {\mathbb{Z}_4} \)-invariant subalgebra of the affine Lie algebra \( \widehat{{su(4)}} \). Using this, we perform a modified version of a Leznov-Savelev analysis and write down formal expressions for the general solutions to the Pohlmeyer reduced AdS5 theory. This analysis relies on the a certain decomposition for the exponentiated algebra elements.