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

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 $T^{\qty(λ_{1},λ_{2},λ)}_{k}$ 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.

arXiv comment12 pages; One reference added; Accepted for publication in Physics Letters B (PLB)

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• Evidence for a $4$-dimensional $\mathcal{N}=1$ integrable quiver in massive type IIA
• Chaotic string dynamics in Bosonic $\eta$-deformed $Ad{S}_5\times T^{1,1}$ background
• Non-Integrability of Strings in $Ad{S}_6\times S^2\times \Sigma$ Background and its 5D Holographic Duals