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Geometric aspects of the ODE/IM correspondence.

Dorey, Patrick E. and Dunning, Clare and Negro, Stefano and Tateo, Roberto (2020) 'Geometric aspects of the ODE/IM correspondence.', Journal of physics A: mathematical and theoretical., 53 (2). p. 223001.


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
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:The deposited manuscript is available under a CC BY-NC-ND 4.0 licence.
Date accepted:26 March 2020
Date deposited:14 May 2020
Date of first online publication:13 May 2020
Date first made open access:13 May 2021

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