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

TL;DR

This paper investigates the integrability properties of the Arutyunov-Bassi-Lacroix (ABL) string sigma model using gauge/string duality, revealing nonintegrability in the full model but integrability in a specific decoupled limit.

Contribution

It provides a comprehensive analysis of the ABL model's (non)integrability using multiple methods, including numerical analysis and Lax pairs, and identifies conditions for integrability.

Findings

Liouvillian nonintegrability of the full sigma model

Analytic integrability in the generalized decoupling limit

Complementary analysis methods confirm results

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.