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

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

2011-05-16

arxiv.org/abs/1105.3227v1

JHEP 1109:002,2011

Physics

High Energy Physics

High Energy Physics - Theory

29 pages + 7 pages appendices

Scientific paper

10.1007/JHEP09(2011)002

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.

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