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Geometric aspects of the ODE/IM correspondence

Dorey, Patrick, Dunning, Clare, Negro, Stefano, Tateo, Roberto (2020) Geometric aspects of the ODE/IM correspondence. Journal of Physics A: Mathematical and Theoretical, 53 . ISSN 0305-4470. (doi:10.1088/1751-8121/ab83c9) (KAR id:80653)


This review describes a link between Lax operators, embedded surfaces and Thermodynamic Bethe Ansatz equations for integrable quantum field theories. This surprising connection between classical and quantum models is undoubtedly one of the most striking discoveries that emerged from the off-critical generalisation of the ODE/IM correspondence, which initially involved only conformal invariant quantum field theories. We will mainly focus of the KdV and sinh-Gordon models. However, various aspects of other interesting systems, such as affine Toda field theories and non-linear sigma models, will be mentioned. We also discuss the implications of these

ideas in the AdS/CFT context, involving minimal surfaces and Wilson loops. This work is a follow-up of the ODE/IM review published more than ten years ago by JPA, before the discovery of its off-critical generalisation and the corresponding geometrical interpretation.

(Partially based on lectures given at the “Young Researchers Integrability School 2017”, in Dublin.)

Item Type: Article
DOI/Identification number: 10.1088/1751-8121/ab83c9
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Clare Dunning
Date Deposited: 30 Mar 2020 10:07 UTC
Last Modified: 04 Mar 2024 15:28 UTC
Resource URI: (The current URI for this page, for reference purposes)

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