Opers for Higher States of the Quantum Boussinesq Model

Masoero, Davide; Raimondo, Andrea

doi:10.1007/978-3-030-57000-2_5

Cited by 9 publications

(10 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, let us mention that the ODE/IM correspondence exist also for the (generalised) Quantum g-KdV models, where g is an untwisted Kac-Moody algebra (the Quantum KdV model coincides with the case g = sl (1) 2 ), and massive deformations of these models [9,25]. In the massless case, the analogous of the monster potentials are called Quantum KdV JHEP02(2021)059 opers, they were introduced by Feigin and Frenkel in [18] and explicitly constructed in [26,27]. Of these opers very little is known and the analogous of the BLZ system exists, but it is too intricate to be manipulated by hand.…”

Section: Discussionmentioning

confidence: 99%

“…Building on this work and using heavily the theory of opers, the analogue of the monster potentials and of the BLZ system (1.1) are explicitly described in [26] in the case g = g (1) , with g a simply-laced simple Lie algebra. The sub-case g = sl (1) 3 is treated with more elementary techniques in [27]. In the present work, we do not study such generalisations.…”

Section: Jhep02(2021)059mentioning

confidence: 99%

See 1 more Smart Citation

Counting monster potentials

Conti

Masoero

2021

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We study the large momentum limit of the monster potentials of Bazhanov-Lukyanov-Zamolodchikov, which — according to the ODE/IM correspondence — should correspond to excited states of the Quantum KdV model.We prove that the poles of these potentials asymptotically condensate about the complex equilibria of the ground state potential, and we express the leading correction to such asymptotics in terms of the roots of Wronskians of Hermite polynomials.This allows us to associate to each partition of N a unique monster potential with N roots, of which we compute the spectrum. As a consequence, we prove — up to a few mathematical technicalities — that, fixed an integer N , the number of monster potentials with N roots coincides with the number of integer partitions of N , which is the dimension of the level N subspace of the quantum KdV model. In striking accordance with the ODE/IM correspondence.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Jhep02(2021)059mentioning

confidence: 99%

Counting monster potentials

Conti

Masoero

2021

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Similar to how the quantum KdV integrable structure is obtained from a reduction of the AKNS one, the Bullough-Dodd can be derived through a reduction of the quantum Boussinesq integrable structure [35,36]. The system of algebraic equations whose solution sets label the eigenstates for the Boussinesq integrable structure was obtained recently in the works [37,38]. In this case the eigenvalues of the reflection operator are expressed in terms of the connection coefficients of a certain class of third order ODEs.…”

Section: Discussionmentioning

confidence: 98%

Spectrum of the reflection operators in different integrable structures

Kotousov¹,

Lukyanov

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

The reflection operators are the simplest examples of the non-local integrals of motion, which appear in many interesting problems in integrable CFT. For the so-called Fateev, quantum AKNS, paperclip and KdV integrable structures, they are built from the (chiral) reflection S-matrices for the Liouville and cigar CFTs. Here we give the full spectrum of the reflection operators associated with these integrable structures. We also obtained a relation between the reflection S-matrices of the cigar and Liouville CFTs. The results of this work are applicable for the description of the scaling behaviour of the Bethe states in exactly solvable lattice systems and may be of interest to the study of the Generalized Gibbs Ensemble associated with the above mentioned integrable structures.

show abstract

“…Finally, let us mention that the ODE/IM correspondence exist also for the (generalised) Quantum g-KdV models, where g is an untwisted Kac-Moody algebra (the Quantum KdV model coincides with the case g = sl 2 ), and massive deformations of these models [24,9]. In the massless case, the analogous of the monster potentials are called Quantum KdV opers, they were introduced by Feigin and Frenkel in [17] and explicitly constructed in [25,26]. Of these opers very little is known and the analogous of the BLZ system exists, but it is too intricate to be manipulated by hand.…”

Section: Discussionmentioning

confidence: 99%

Counting monster potentials

Conti,

Masoero

2020

Preprint

Self Cite

View full text Add to dashboard Cite

We study the large momentum limit of the monster potentials of Bazhanov-Lukyanov-Zamolodchikov, which -according to the ODE/IM correspondence -should correspond to excited states of the Quantum KdV model.We prove that the poles of these potentials asymptotically condensate about the complex equilibria of the ground state potential, and we express the leading correction to such asymptotics in terms of the roots of Wronskians of Hermite polynomials.This allows us to associate to each partition of N a unique monster potential with N roots, of which we compute the spectrum. As a consequence, we prove -up to a few mathematical technicalities -that, fixed an integer N , the number of monster potentials with N roots coincides with the number of integer partitions of N , which is the dimension of the level N subspace of the quantum KdV model. In striking accordance with the ODE/IM correspondence. Contents1. Introduction 1 2. First Considerations 5 3. Rational extensions of the harmonic oscillator and related problems 8 4. On large solutions 10 5. The higher-state-potentials in the large momentum limit 13 6. Perturbation Series. The non-degenerate case 22 7. Perturbation Series. Completely degenerate case 24 8. Perturbation Series. Partially degenerate case 30 9. Integer 2 alpha 32 10. Numerics 36 11. Concluding Remarks 38 12. Appendix 39 References 47

show abstract

Opers for Higher States of the Quantum Boussinesq Model

Cited by 9 publications

References 13 publications

Counting monster potentials

Counting monster potentials

Spectrum of the reflection operators in different integrable structures

Counting monster potentials

Contact Info

Product

Resources

About