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Geometric aspects of the ODE/IM correspondence

Dorey, Patrick E; Dunning, Clare; Negro, Stefano; Tateo, Roberto

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Clare Dunning

Stefano Negro

Roberto Tateo


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.)


Dorey, P. E., Dunning, C., Negro, S., & Tateo, R. (2020). Geometric aspects of the ODE/IM correspondence. Journal of Physics A: Mathematical and Theoretical, 53(2), Article 223001.

Journal Article Type Article
Acceptance Date Mar 26, 2020
Online Publication Date May 13, 2020
Publication Date Jun 5, 2020
Deposit Date Mar 30, 2020
Publicly Available Date May 13, 2021
Journal Journal of Physics A: Mathematical and Theoretical
Print ISSN 1751-8113
Electronic ISSN 1751-8121
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 53
Issue 2
Article Number 223001
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