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Analytic (non)integrability of Arutyunov-Bassi-Lacroix model

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arxiv 2106.01237 v2 pith:DVG74TQ7 submitted 2021-06-02 hep-th

Jitendra Pal , Arnab Mukherjee , Arindam Lala , Dibakar Roychowdhury This is my paper · ORCID
classification hep-th
keywords analysisintegrabilitylambdamodelstringanalyticarutyunov-bassi-lacroixliouvillian
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abstract

We use the notion of the gauge/string duality and discuss the Liouvillian (non) integrability criteria for string sigma models in the context of recently proposed Arutyunov-Bassi-Lacroix (ABL) model [JHEP \textbf{03} (2021), 062]. Our analysis complements those previous results due to numerical analysis as well as Lax pair formulation. We consider a winding string ansatz for the deformed torus $T^{\qty(\lambda_{1},\lambda_{2},\lambda)}_{k}$ which can be interpreted as a system of coupled pendulums. Our analysis reveals the Liouvillian nonintegrablity of the associated sigma model. We also obtain the \emph{generalized} decoupling limit and confirm the analytic integrability for the decoupled sector.

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    Only the sinusoidal quiver α(z)=A sin(ωz) in the new massive type IIA AdS5 family shows no chaotic signatures, providing suggestive evidence for its classical integrability.

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