On purely transmitting defects in affine Toda field theory

Abstract

Affine Toda field theories with a purely transmitting integrable defect are considered and the model based on a_2 is analysed in detail. After providing a complete characterization of the problem in a classical framework, a suitable quantum transmission matrix, able to describe the interaction between an integrable defect and solitons, is found. Two independent paths are taken to reach the result. One is an investigation of the triangle equations using the S-matrix for the imaginary coupling bulk affine Toda field theories proposed by Hollowood, and the other uses a functional integral approach together with a bootstrap procedure. Evidence to support the results is collected in various ways: for instance, through the calculation of the transmission factors for the lightest breathers. While previous discoveries within the sine-Gordon model motivated this study, there are several new phenomena displayed in the a_2 model including intriguing disparities between the classical and the quantum pictures. For example, in the quantum framework, for a specific range of the coupling constant that excludes a neighbourhood of the classical limit, there is an unstable bound state.

36 pages

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• The sine-Gordon model with integrable defects revisited
• Integrable defects in affine Toda field theory and infinite dimensional representations of quantum groups
• Sigma models in the presence of dynamical point-like defects
• Defects in the discrete non-linear Schrodinger model
• Form factors in the presence of integrable defects
• Momentum conserving defects in affine Toda field theories
• Defect scaling Lee-Yang model from the perturbed DCFT point of view
• Finite volume form factors in the presence of integrable defects
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• Type-I integrable quantum impurities in the Heisenberg model
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• Jumps and twists in affine Toda field theories
• Defect fusing rules in affine Toda field theory
• Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains
• Transmission amplitudes from Bethe ansatz equations
• Defects and Dressed Boundaries in Complex Sine-Gordon Theory
• Aspects of defects in integrable quantum field theory
• Quantum anomalies in A^{(1)}_r Toda theories with defects
• Type II defects revisited
• The sine-Gordon model in the presence of defects