Classical versus quantum symmetries for Toda theories with a nontrivial boundary perturbation

Penati, Silvia; Refolli, Andrea; Zanon, D.

doi:10.1016/0550-3213(96)00163-0

Cited by 7 publications

(17 citation statements)

References 55 publications

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“…In conclusion, in the presence of a line of defects classical integrability survives if the bulk conservation laws (2.8) are supplemented by boundary conditions (2.16). This generalizes what happens in two-dimensional theories with a boundary [37][38][39][40][41][42]. In fact, the present case reduces to that one if we set one type of fields to zero, for instance φ (−) a = 0 for any a.…”

Section: Jhep06(2019)062supporting

confidence: 71%

“…Over the past years the study of integrability properties has been generalized to Toda models with boundaries [34][35][36]. This has been implemented both at classical [37][38][39] and quantum [40][41][42] level. While in the classical case it is possible to select a particular class of boundary perturbations that preserve an infinite number of conserved charges, at quantum level the situation is more involved.…”

Section: Jhep06(2019)062mentioning

confidence: 99%

“…This allows to preserve spin-4 current in the sinh-Gordon model and spin-3 current in A (1) r>1 models, as well as spin-4 current in nonsimply-laced Toda theories. However, strong indications arise [42] that conservation of higher-spin currents might get irreparably affected by anomalies, no matter the choice of the boundary potential.…”

Section: Jhep06(2019)062mentioning

confidence: 99%

“…Toda theories with a line of defect, we compute the quantum conservation laws for energy, momentum and the first higher-spin current which is conserved at classical level, that is spin-4 for sine-Gordon and spin-3 for A (1) r>1 Toda models. We apply massless perturbation theory used in [40][41][42] for theories with boundaries to evaluate conservation laws at all orders in the coupling constant. As already experienced in theories with boundaries, also in the present case anomalous contributions arise from quantum loops.…”

Section: Jhep06(2019)062mentioning

confidence: 99%

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Quantum anomalies in A(1) r Toda theories with defects

Penati

Polvara

2019

J. High Energ. Phys.

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We study quantum integrability of affine Toda theories with a line of defect. In particular, we focus on the problem of constructing quantum higher-spin conserved currents in models defined by two A (1) r Toda theories separated by a non-trivial type-I defect. For a suitable choice of the defect potential these theories are known to be classically integrable, that is they possess an infinite set of higher-spin conserved charges in involution. Studying the corresponding conservation laws at quantum level we discover that anomalies arise, which we compute exactly at all orders in the coupling constant. While for the stress-energy tensor these anomalies can be cancelled by a finite renormalization of the defect potential, we find that from the first non-trivial higher-spin current this is no longer possible. This opens the question whether these theories are indeed integrable at quantum level.

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Section: Jhep06(2019)062supporting

confidence: 71%

Section: Jhep06(2019)062mentioning

confidence: 99%

Section: Jhep06(2019)062mentioning

confidence: 99%

Section: Jhep06(2019)062mentioning

confidence: 99%

See 2 more Smart Citations

Quantum anomalies in A(1) r Toda theories with defects

Penati

Polvara

2019

J. High Energ. Phys.

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“…Once the quantum action is determined the quantum energy is defined by 22) and the WKB quantisation condition states that…”

Section: Semi-classical Quantisationmentioning

confidence: 99%

Boundary breathers in the sinh-Gordon model

Corrigan

Delius

1999

J. Phys. A: Math. Gen.

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We present an investigation of the boundary breather states of the sinh-Gordon model restricted to a half-line. The classical boundary breathers are presented for a two parameter family of integrable boundary conditions. Restricting to the case of boundary conditions which preserve the φ → −φ symmetry of the bulk theory, the energy spectrum of the boundary states is computed in two ways: firstly, by using the bootstrap technique and subsequently, by using a WKB approximation. Requiring that the two descriptions of the spectrum agree with each other allows a determination of the relationship between the boundary parameter, the bulk coupling constant, and the parameter appearing in the reflection factor derived by Ghoshal to describe the scattering of the sinh-Gordon particle from the boundary.

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Tree level integrability in 2d quantum field theories and affine Toda models

Dorey

Polvara

2022

J. High Energ. Phys.

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We investigate the perturbative integrability of massive (1+1)-dimensional bosonic quantum field theories, focusing on the conditions for them to have a purely elastic S-matrix, with no particle production and diagonal scattering, at tree level. For theories satisfying what we call ‘simply-laced scattering conditions’, by which we mean that poles in inelastic 2 to 2 processes cancel in pairs, and poles in allowed processes are only due to one on-shell propagating particle at a time, the requirement that all inelastic amplitudes must vanish is shown to imply the so-called area rule, connecting the 3-point couplings $$ {C}_{abc}^{(3)} $$ C abc 3 to the masses ma, mb, mc of the coupled particles in a universal way. We prove that the constraints we find are universally satisfied by all affine Toda theories, connecting pole cancellations in amplitudes to properties of the underlying root systems, and develop a number of tools that we expect will be relevant for the study of loop amplitudes.

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Classical versus quantum symmetries for Toda theories with a nontrivial boundary perturbation

Abstract: IFUM-522-FT

Cited by 7 publications

References 55 publications

Quantum anomalies in A(1) r Toda theories with defects

Quantum anomalies in A(1) r Toda theories with defects

Boundary breathers in the sinh-Gordon model

Tree level integrability in 2d quantum field theories and affine Toda models

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