General Leznov-Savelev solutions for Pohlmeyer reduced AdS${}_5$ minimal surfaces

Abstract

We consider the Pohlmeyer reduced sigma model describing AdS${}_5$ 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 Laznov-Savelev analysis, which allows us to write formal expressions for the general solutions for the Pohlmeyer reduced AdS${}_5$ theory. This analysis relies on the a certain decomposition for the exponentiated algebra elements.

29 pages + 7 pages appendices

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