Bethe Ansatz equations for the classical $A_n^{(1)}$ affine Toda field theories

Adamopoulou, Panagiota; Dunning, Clare

doi:10.48550/arxiv.1401.1187

Cited by 6 publications

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“…Recently the massive ODE/IM correspondence has been generalized to a class of modified affine Toda field equations [10,11,12,13,14,15]. In particular, Locke and one of the present authors studied the modified affine Toda equations for affine Lie algebra ĝ∨ , where ĝ is an untwisted affine Lie algebra including exceptional type [13].…”

Section: Introductionmentioning

confidence: 99%

ODE/IM correspondence and modified affine Toda field equations

Ito

Locke

2014

Nuclear Physics B

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We study the two-dimensional affine Toda field equations for affine Lie algebra $\hat{\mathfrak{g}}$ modified by a conformal transformation and the associated linear equations. In the conformal limit, the associated linear problem reduces to a (pseudo-)differential equation. For classical affine Lie algebra $\hat{\mathfrak{g}}$, we obtain a (pseudo-)differential equation corresponding to the Bethe equations for the Langlands dual of the Lie algebra $\mathfrak{g}$, which were found by Dorey et al. in study of the ODE/IM correspondence.Comment: 29 pages; added references and note, fixed typos, minor rewritin

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Section: Introductionmentioning

confidence: 99%

ODE/IM correspondence and modified affine Toda field equations

Ito

Locke

2014

Nuclear Physics B

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“…These results were extended to massive Integrable Quantum Field Theories (IQFT) [27] (for recent developments, see also refs. [28][29][30][31][32][33][34][35]). The general relation of this type will be referred to in the paper as the ODE/IQFT correspondence.…”

Section: Introductionmentioning

confidence: 99%

Quantum transfer-matrices for the sausage model

Bazhanov

Kotousov

Lukyanov

2018

J. High Energ. Phys.

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In this work we revisit the problem of the quantization of the two-dimensional O(3) non-linear sigma model and its one-parameter integrable deformation -the sausage model. Our consideration is based on the so-called ODE/IQFT correspondence, a variant of the Quantum Inverse Scattering Method. The approach allowed us to explore the integrable structures underlying the quantum O(3)/sausage model. Among the obtained results is a system of non-linear integral equations for the computation of the vacuum eigenvalues of the quantum transfer-matrices.

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“…We wish however to note that for general n the matrices U and Ū entering the GW system (131) can be seen to belong to the a ne untwisted Kač-Moody algebra of type B or C. By appropriately redefining the quantities listed above, one can connect this system with the corresponding Toda field theory. O -critical generalisations of the ODE/IM correspondence associated to higher-rank algebras have been discussed in [67][68][69][70][71][72][73][74], although without specific analysis of the connection with surface embedding. The case we focus on here, that is n = 2, is particularly simple as the associated algebra turns out to be B…”

Section: Surfaces Embedded In Ads N+1mentioning

confidence: 99%

Geometric aspects of the ODE/IM correspondence

Dorey¹,

Dunning²,

Negro³

et al. 2020

J. Phys. A: Math. Theor.

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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 o -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 a ne 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 o -critical generalisation and the corresponding geometrical interpretation.(Partially based on lectures given at the "Young Researchers Integrability School 2017", in Dublin.) 1 arXiv:1911.13290v2 [hep-th]

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Bethe Ansatz equations for the classical $A_n^{(1)}$ affine Toda field theories

Cited by 6 publications

References 0 publications

ODE/IM correspondence and modified affine Toda field equations

ODE/IM correspondence and modified affine Toda field equations

Quantum transfer-matrices for the sausage model

Geometric aspects of the ODE/IM correspondence

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