Counting monster potentials

Conti, Riccardo; Masoero, Davide

doi:10.1007/jhep02(2021)059

Cited by 15 publications

(13 citation statements)

References 28 publications

(119 reference statements)

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“…soliton solutions, and the link with the ODE/IM correspondence [37][38][39][40]. Understanding, at a deeper level, the TT-like deformations of quantum spin-chains [41][42][43][44], possibly within the Quantum Spectral Curve framework of AdS/CFT [45][46][47][48][49][50], is also an unexplored avenue that might lead to unexpected and exciting discoveries.…”

Section: Jhep04(2021)121mentioning

confidence: 99%

$$ \mathrm{T}\overline{\mathrm{T}} $$-deformed nonlinear Schrödinger

Ceschin

Conti

Tateo

2021

J. High Energ. Phys.

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The $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ -deformed classical Lagrangian of a 2D Lorentz invariant theory can be derived from the original one, perturbed only at first order by the bare $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ composite field, through a field-dependent change of coordinates. Considering, as an example, the nonlinear Schrödinger (NLS) model with generic potential, we apply this idea to non-relativistic models. The form of the deformed Lagrangian contains a square-root and is similar but different from that for relativistic bosons. We study the deformed bright, grey and Peregrine’s soliton solutions. Contrary to naive expectations, the $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ -perturbation of nonlinear Schrödinger NLS with quartic potential does not trivially emerge from a standard non-relativistic limit of the deformed sinh-Gordon field theory. The c → ∞ outcome corresponds to a different type of irrelevant deformation. We derive the corresponding Poisson bracket structure, the equations of motion and discuss various interesting aspects of this alternative type of perturbation, including links with the recent literature.

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Section: Jhep04(2021)121mentioning

confidence: 99%

$$ \mathrm{T}\overline{\mathrm{T}} $$-deformed nonlinear Schrödinger

Ceschin

Conti

Tateo

2021

J. High Energ. Phys.

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“…Considering the left-hand-side of the above expression as a Riemann-Stieltjes integral, we write 10 . Integrating (c) by parts we obtain…”

Section: Integral Bethe Ansatzmentioning

confidence: 99%

“…. , H} (2.6b) 10 The latter formula stems from the fact that z(x) − 1 2 is constant on every interval of the form…”

Section: Integral Bethe Ansatzmentioning

confidence: 99%

“…In this Section we briefly introduce the ODE/IM correspondence for the Quantum KdV/Monster potentials; the interested reader can read more details in [13], which is the standard reference for early results in this theory, or in [7] or in [10].…”

Section: On the Ode/im Correspondencementioning

confidence: 99%

“…In fact in our previous paper [10], we proved -assuming the existence of a certain Puiseaux series as per Conjecture 5.9 in [10] -that monster potentials with N apparent singularities, are parametrised by partitions of N and we computed the large momentum asymptotics of the eigenvalues, that turn out to be real and positive in this regime. As a consequence, combining the result of [10] with the results of the present paper (in particular, comparing the two large momentum asymptotics that we have found), we prove -up to Conjecture 5.9 in [10] -that the monster potentials are complete: For every solution of the BAE with real and 2 The ODE/IM correspondence can be thus thought of as a Hilbert-Polya conjecture for the BAE. The distribution of Bethe roots turns out to be much more regular than the distribution of non trivial zeroes of the zeta function.…”

Section: Introductionmentioning

confidence: 97%

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On solutions of the Bethe Ansatz for the Quantum KdV model

Conti¹,

Masoero²

2021

Preprint

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We study the Bethe Ansatz equations for the Quantum KdV model, which are also known to be solved by the spectrum of a family of anharmonic oscillators known as monster potentials (ODE/IM correspondence).These Bethe Ansatz equations depend on two parameters which we can identify with the momentum and the degree at infinity of the anharmonic oscillators. We provide a complete classification of the solutions with only real and positive roots -when the degree is greater than 2 -in terms of admissible sequences of holes: We prove that admissible sequences of holes are naturally parametrised by integer partitions, and we prove that to each admissible sequence of holes (i.e. to each partition) there corresponds a unique solution of the Bethe Ansatz equations, if the momentum is large enough.Consequently, we deduce that the monster potentials are complete, in the sense that every solution of the Bethe Ansatz Equations coincides with the spectrum of a unique monster potential. This essentially (i.e. up to gaps in the previous literature) proves the ODE/IM correspondence for the Quantum KdV model/Monster potentials -which was conjectured by Dorey-Tateo and Bazhanov-Lukyanov-Zamolodchikov -when the degree is greater than 2.Our approach is based on the transformation of the the Bethe Ansatz Equations into a free-boundary nonlinear integral equation -akin to the equations known in the physics literature as DDV or BKP or NLIE -of which we develop the mathematical theory from the beginning.

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Deforming the ODE/IM correspondence with $$ \textrm{T}\overline{\textrm{T}} $$

Fabrizio

Nicolò

Negro

et al. 2023

J. High Energ. Phys.

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The ODE/IM correspondence is an exact link between classical and quantum integrable models. The primary purpose of this work is to show that it remains valid after $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ perturbation on both sides of the correspondence. In particular, we prove that the deformed Lax pair of the sinh-Gordon model, obtained from the unperturbed one through a dynamical change of coordinates, leads to the same Burgers-type equation governing the quantum spectral flow induced by $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ . Our main conclusions have general validity, as the analysis may be easily adapted to all the known ODE/IM examples involving integrable quantum field theories.

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Counting monster potentials

Cited by 15 publications

References 28 publications

$$ \mathrm{T}\overline{\mathrm{T}} $$-deformed nonlinear Schrödinger

$$ \mathrm{T}\overline{\mathrm{T}} $$-deformed nonlinear Schrödinger

On solutions of the Bethe Ansatz for the Quantum KdV model

Deforming the ODE/IM correspondence with $$ \textrm{T}\overline{\textrm{T}} $$

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