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

Gleb Arutyunov·Marija Zamaklar
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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.

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Gleb Arutyunov, Marija Zamaklar. 2005-04-18. Linking Backlund and Monodromy Charges for Strings on AdS_5 x S^5. https://doi.org/10.1088/1126-6708%2F2005%2F07%2F026

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