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.

Geometric aspects of the ODE/IM correspondence

Negro S.;Tateo R.
2020-01-01

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.
2020
53
22
223001
223065
https://inspirehep.net/literature/1767757
AdS/CFT; integrable systems; minimal surfaces; ODE/IM correspondence
Dorey P.; Dunning C.; Negro S.; Tateo R.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1762893
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