Reflection factors and a two-parameter family of boundary bound states in the sinh-Gordon model

E Corrigan; A Taormina

Reflection factors and a two-parameter family of boundary bound states in the sinh-Gordon model

Mathematics

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Abstract

The investigation of boundary breather states of the sinh-Gordon model restricted to a half-line is revisited. Properties of the classical boundary breathers for the two-parameter family of integrable boundary conditions are reviewed and extended. The energy spectrum of the quantized boundary states is computed, firstly by using a bootstrap technique and, subsequently using a WKB approximation. Requiring that the two descriptions of the spectrum agree with one another allows a determination of the relationship between the boundary parameters, the bulk coupling constant, and the two parameters appearing in the reflection factor describing the scattering of the sinh-Gordon particle from the boundary. These calculations had been performed previously for the case in which the boundary conditions preserve the bulk Zz symmetry of the model. The significantly more difficult case of general boundary conditions which violate the bulk symmetry is treated in this paper. The results clarify the weak-strong-coupling duality of the sinh-Gordon model with integrable boundary conditions.

Original language	English
Pages (from-to)	8739-8754
Number of pages	16
Journal	Journal of Physics A: Mathematical and General
Volume	33
Issue number	48
Publication status	Published - 8 Dec 2000

Keywords

TODA FIELD-THEORY
S-MATRICES

Cite this

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title = "Reflection factors and a two-parameter family of boundary bound states in the sinh-Gordon model",

abstract = "The investigation of boundary breather states of the sinh-Gordon model restricted to a half-line is revisited. Properties of the classical boundary breathers for the two-parameter family of integrable boundary conditions are reviewed and extended. The energy spectrum of the quantized boundary states is computed, firstly by using a bootstrap technique and, subsequently using a WKB approximation. Requiring that the two descriptions of the spectrum agree with one another allows a determination of the relationship between the boundary parameters, the bulk coupling constant, and the two parameters appearing in the reflection factor describing the scattering of the sinh-Gordon particle from the boundary. These calculations had been performed previously for the case in which the boundary conditions preserve the bulk Zz symmetry of the model. The significantly more difficult case of general boundary conditions which violate the bulk symmetry is treated in this paper. The results clarify the weak-strong-coupling duality of the sinh-Gordon model with integrable boundary conditions.",

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T1 - Reflection factors and a two-parameter family of boundary bound states in the sinh-Gordon model

AU - Corrigan, E

AU - Taormina, A

PY - 2000/12/8

Y1 - 2000/12/8

N2 - The investigation of boundary breather states of the sinh-Gordon model restricted to a half-line is revisited. Properties of the classical boundary breathers for the two-parameter family of integrable boundary conditions are reviewed and extended. The energy spectrum of the quantized boundary states is computed, firstly by using a bootstrap technique and, subsequently using a WKB approximation. Requiring that the two descriptions of the spectrum agree with one another allows a determination of the relationship between the boundary parameters, the bulk coupling constant, and the two parameters appearing in the reflection factor describing the scattering of the sinh-Gordon particle from the boundary. These calculations had been performed previously for the case in which the boundary conditions preserve the bulk Zz symmetry of the model. The significantly more difficult case of general boundary conditions which violate the bulk symmetry is treated in this paper. The results clarify the weak-strong-coupling duality of the sinh-Gordon model with integrable boundary conditions.

AB - The investigation of boundary breather states of the sinh-Gordon model restricted to a half-line is revisited. Properties of the classical boundary breathers for the two-parameter family of integrable boundary conditions are reviewed and extended. The energy spectrum of the quantized boundary states is computed, firstly by using a bootstrap technique and, subsequently using a WKB approximation. Requiring that the two descriptions of the spectrum agree with one another allows a determination of the relationship between the boundary parameters, the bulk coupling constant, and the two parameters appearing in the reflection factor describing the scattering of the sinh-Gordon particle from the boundary. These calculations had been performed previously for the case in which the boundary conditions preserve the bulk Zz symmetry of the model. The significantly more difficult case of general boundary conditions which violate the bulk symmetry is treated in this paper. The results clarify the weak-strong-coupling duality of the sinh-Gordon model with integrable boundary conditions.

KW - TODA FIELD-THEORY

KW - S-MATRICES

M3 - Article

SN - 0305-4470

VL - 33

SP - 8739

EP - 8754

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 48

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