Linking Backlund and Monodromy Charges for Strings on AdS_5 x S^5

TL;DR

This paper establishes a direct relation between Backlund and monodromy methods for generating conserved charges in the string sigma model on AdS_5 x S^5, enhancing understanding of integrability in this context.

Contribution

It explicitly connects Backlund transformations with monodromy-based conserved charges, providing a non-perturbative solution and clarifying their interplay in the string sigma model.

Findings

Backlund transformations generate solutions compatible with Virasoro constraints at a special parameter value.

The generating functional of Backlund conservation laws equals a sum of quasi-momenta.

Quasi-momenta positions are determined by the Backlund transform parameter.

Abstract

We find an explicit relation between the two known ways of generating an infinite set of local conserved charges for the string sigma model on AdS_5 x S^5: the Backlund and monodromy approaches. We start by constructing the two-parameter family of Backlund transformations for the string with an arbitrary world-sheet metric. We then show that only for a special value of one of the parameters the solutions generated by this transformation are compatible with the Virasoro constraints. By solving the Backlund equations in a non-perturbative fashion, we finally show that the generating functional of the Backlund conservation laws is equal to a certain sum of the quasi-momenta. The positions of the quasi-momenta in the complex spectral plane are uniquely determined by the real parameter of the Backlund transform.