Analytic integrability for strings on $ \eta $ and $ \lambda $ deformed backgrounds

TL;DR

This paper investigates the integrability of classical string configurations in eta and lambda deformed backgrounds, finding non-integrability in eta deformations and integrability in lambda deformations, impacting dual gauge theory spectra.

Contribution

It provides the first analytic comparison of integrability conditions between eta and lambda deformed string backgrounds, revealing a stark contrast in their integrability properties.

Findings

Eta deformed backgrounds are non-integrable for classical strings.

Lambda deformed backgrounds are integrable for classical strings.

Results constrain the operator spectrum in dual gauge theories at strong coupling.

Abstract

In this paper, based on simple analytic techniques, we explore the integrability conditions for classical stringy configurations defined over $ \eta $ as well as $ \lambda $- deformed backgrounds. We perform our analysis considering classical string motions within various subsectors of the full target space geometry. It turns out that classical string configurations defined over $ \eta $- deformed backgrounds are non-integrable whereas on the other hand, the corresponding configurations are integrable over the $ \lambda $- deformed background. Our analysis therefore imposes a strong constraint on the operator spectrum associated with the corresponding dual gauge theories at strong coupling.