Geometric aspects of the ODE/IM correspondence

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

Abstract

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.)

Citation

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. https://doi.org/10.1088/1751-8121/ab83c9

• 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
• DOI: https://doi.org/10.1088/1751-8121/ab83c9
• Public URL: https://durham-repository.worktribe.com/output/1273840
• Related Public URLs: https://arxiv.org/abs/1911.13290