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

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JournalNuclear Physics B
DatePublished - 21 Jul 2011
Issue number3
Volume848
Number of pages33
Pages (from-to)545-577
Original languageEnglish

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.

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