ABCD and ODEs

Dorey, Patrick; Dunning, Clare; Masoero, Davide; Suzuki, Junji; Tateo, Roberto

doi:10.1007/978-90-481-2810-5_45

Cited by 4 publications

(4 citation statements)

References 22 publications

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“…It would be natural to extend our work to other Lie algebras [65][66][67]. The definition of the Kondo defects is valid for any Lie algebra, with an important caveat: the matrices t a do not have to be generators of the Lie algebra, they only need to transform in the adjoint representation of the global symmetry group.…”

Section: Higher Rankmentioning

confidence: 99%

Kondo line defects and affine Gaudin models

Gaiotto¹,

Lee²,

Wu³

2020

Preprint

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Section: Higher Rankmentioning

confidence: 99%

Kondo line defects and affine Gaudin models

Gaiotto¹,

Lee²,

Wu³

2020

Preprint

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“…In [13] and [14], the spectral link between H 2 and H 3 was naturally extended to the adjoint operator H † 3 to (2.8):…”

Section: Isospectral Second and Third Order Eigenproblemsmentioning

confidence: 99%

Quasi-exact solvability, resonances and trivial monodromy in ordinary differential equations

Dorey¹,

Dunning²,

Tateo³

2012

J. Phys. A: Math. Theor.

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A correspondence between the sextic anharmonic oscillator and a pair of thirdorder ordinary differential equations is used to investigate the phenomenon of quasi-exact solvability for eigenvalue problems involving differential operators with order greater than 2. In particular, links with Bender-Dunne polynomials and resonances between independent solutions are observed for certain secondorder cases, and extended to the higher-order problems.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Quantum physics with non-Hermitian operators'.

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“…The analysis undertaken in this work can be likened to a lateral problem. On the other hand, findings from a reference like [3] (specifically section 6, page 262, penultimate paragraph) seem to suggest that the Riemann ζ function might manifest itself as a spectral determinant in what appears to be a spectral central problem (for a comparison, see, for example, [14] or the appendix B.2 of [15]), possibly entailing boundary conditions on the multivalued wave functions that involve analytic continuation onto the other Riemann sheets.…”

Section: Discussionmentioning

confidence: 99%

The generalized Born oscillator and the Berry-Keating Hamiltonian

Giordano,

Negro,

Tateo

2023

J. High Energ. Phys.

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In this study, we introduce and investigate a family of quantum mechanical models in 0 + 1 dimensions, known as generalized Born quantum oscillators. These models represent a one-parameter deformation of a specific system obtained by reducing the Nambu-Goto theory to 0 + 1 dimensions. Despite these systems showing significant similarities with $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ -type perturbations of two-dimensional relativistic models, our analysis reveals their potential as interesting regularizations of the Berry-Keating theory. We quantize these models using the Weyl quantization scheme up to very high orders in ħ. By examining a specific scaling limit, we observe an intriguing connection between the generalized Born quantum oscillators and the Riemann-Siegel θ function.

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ABCD and ODEs

Abstract: We outline a relationship between conformal field theories and spectral problems of ordinary differential equations, and discuss its generalisation to models related to classical Lie algebras.

Cited by 4 publications

References 22 publications

Kondo line defects and affine Gaudin models

Kondo line defects and affine Gaudin models

Quasi-exact solvability, resonances and trivial monodromy in ordinary differential equations

The generalized Born oscillator and the Berry-Keating Hamiltonian

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