Bethe ansatz equations for the classical $A^{(1)}_{n}$ affine Toda field theories

Adamopoulou, Panagiota; Dunning, Clare

doi:10.1088/1751-8113/47/20/205205

Cited by 25 publications

(123 citation statements)

References 23 publications

(81 reference statements)

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“…Furthermore, previous work on the massive ODE/IM correspondence in this context on the modified sinh-Gordon equation [8] and A (1) r -type Toda theories [10] are in agreement with this work. A (2) 2r does not fall under the identification (5.1), yet the results for this case also agreed with previous work on the Tzitzéica-Bullough-Dodd equation (the specific case of A (2) 2 ) [9].…”

Section: This Papersupporting

confidence: 91%

“…First, following [8][9][10][11] we consider a special family of solutions to the equation of motion (2.5) φ(ρ, θ) with the following properties:…”

Section: Asymptotic Behaviormentioning

confidence: 99%

“…This was generalized to a relation between the classical Tzitzéica-Bullough-Dodd equation (A (2) 2 algebra) and the quantum Izergin-Korepin model in [9], and was studied for type A (1) r affine Toda theories in [10,11]. In these works it was shown that connection coefficients for subdominant solutions to the linear problem associated with the affine Toda field equation correspond to the vacuum eigenvalues of Q-operators for g-type quantum integrable models.…”

Section: Introductionmentioning

confidence: 99%

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ODE/IM correspondence and Bethe ansatz for affine Toda field equations

Ito

Locke

2015

Nuclear Physics B

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We study the linear problem associated with modified affine Toda field equation for the Langlands dual $\hat{\mathfrak{g}}^\vee$, where $\hat{\mathfrak{g}}$ is an untwisted affine Lie algebra. The connection coefficients for the asymptotic solutions of the linear problem are found to correspond to the $Q$-functions for $\mathfrak{g}$-type quantum integrable models. The $\psi$-system for the solutions associated with the fundamental representations of $\mathfrak{g}$ leads to Bethe ansatz equations associated with the affine Lie algebra $\hat{\mathfrak{g}}$. We also study the $A^{(2)}_{2r}$ affine Toda field equation in massless limit in detail and find its Bethe ansatz equations as well as T-Q relations.Comment: 22 page

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Section: This Papersupporting

confidence: 91%

“…First, following [8][9][10][11] we consider a special family of solutions to the equation of motion (2.5) φ(ρ, θ) with the following properties:…”

Section: Asymptotic Behaviormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

ODE/IM correspondence and Bethe ansatz for affine Toda field equations

Ito

Locke

2015

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: Jhep01(2018)021mentioning

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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“…The ordinary differential equations for the integrable models associated with the Bethe equations of a classical Lie algebra g have been proposed in [19]. For a general Lie algebra g, it is obtained from the conformal limit of the linear problem for the modified affine Toda field equations associated withĝ ∨ , while the full linear problem describes the massive version of the ODE/IM correspondence [20,21,22,23,24,25,26] (see also [27] for a classical Lie algebra case). Hereĝ denotes the untwisted affine Lie algebra of g andĝ ∨ the Langlands dual ofĝ.…”

Section: Introductionmentioning

confidence: 99%

ODE/IM correspondence and the Argyres-Douglas theory

Ito

Shu

2017

J. High Energ. Phys.

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We study the quantum spectral curve of the Argyres-Douglas theories in the Nekrasov-Sahashvili limit of the Omega-background. Using the ODE/IM correspondence we investigate the quantum integrable model corresponding to the quantum spectral curve. We show that the models for the A 2N -type theories are non-unitary coset models (A 1 ) 1 × (A 1 ) L /(A 1 ) L+1 at the fractional level L = 2 2N +1 −2, which appear in the study of the 4d/2d correspondence of N = 2 superconformal field theories. Based on the WKB analysis, we clarify the relation between the Y-functions and the quantum periods and study the exact Bohr-Sommerfeld quantization condition for the quantum periods. We also discuss the quantum spectral curves for the D and E type theories.

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Bethe ansatz equations for the classical $A^{(1)}_{n}$ affine Toda field theories

Cited by 25 publications

References 23 publications

ODE/IM correspondence and Bethe ansatz for affine Toda field equations

ODE/IM correspondence and Bethe ansatz for affine Toda field equations

Quantum transfer-matrices for the sausage model

ODE/IM correspondence and the Argyres-Douglas theory

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