Integrable defects in affine Toda field theory and infinite dimensional representations of quantum groups

Abstract

Transmission matrices for two types of integrable defect are calculated explicitly, first by solving directly the nonlinear transmission Yang-Baxter equations, and second by solving a linear intertwining relation between a finite dimensional representation of the relevant Borel subalgebra of the quantum group underpinning the integrable quantum field theory and a particular infinite dimensional representation expressed in terms of sets of generalized `quantum' annihilation and creation operators. The principal examples analysed are based on the $a_2^{(2)}$ and $a_n^{(1)}$ affine Toda models but examples of similar infinite dimensional representations for quantum Borel algebras for all other affine Toda theories are also provided.

35 pages

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Cited by in corpus (15)

• Folding defect affine Toda field theories
• Momentum conserving defects in affine Toda field theories
• Defect scaling Lee-Yang model from the perturbed DCFT point of view
• Generalized q-Onsager Algebras and Dynamical K-matrices
• Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model
• Finite volume form factors in the presence of integrable defects
• Defects in the supersymmetric mKdV hierarchy via Backlund transformations
• Defect fusing rules in affine Toda field theory
• Integrability of generalised type II defects in affine Toda field theory
• Infinite dimension reflection matrices in the sine-Gordon model with a boundary
• Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains
• Aspects of defects in integrable quantum field theory
• Quantum anomalies in A^{(1)}_r Toda theories with defects
• The classical nonlinear Schrödinger model with a new integrable boundary
• Fusing defect for the N=2 super sinh-Gordon model