Geometric aspects of the ODE/IM correspondence

Patrick Dorey, Clare Dunning, Stefano Negro, Roberto Tateo

Research output: Contribution to journalReview articlepeer-review

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 J. Phys. A: Math. Theor., before the discovery of its off-critical generalisation and the corresponding geometrical interpretation.

Original languageEnglish
Article number223001
JournalJournal of Physics A: Mathematical and Theoretical
Volume53
Issue number22
Early online date13 May 2020
DOIs
Publication statusPublished - 5 Jun 2020

Bibliographical note

Publisher Copyright:
© 2020 IOP Publishing Ltd.

Keywords

  • AdS/CFT
  • integrable systems
  • minimal surfaces
  • ODE/IM correspondence

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