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Root Systems and Purely Elastic S-Matrices II
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Starting from a recently-proposed general formula, various properties of the ADE series of purely elastic S-matrices are rederived in a universal way. In particular, the relationship between the pole structure and the bootstrap equations is shown to follow from properties of root systems. The discussion leads to a formula for the signs of the three-point couplings in the simply-laced affine Toda theories, and a simple proof of a result due to Klassen and Melzer of relevance to Thermodynamic Bethe Ansatz calculations.
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One-loop integrability with shifting masses
Tree-level elastic 2d theories with polynomial interactions remain elastic at one loop once masses are renormalized by bubble diagrams, with a universal one-loop S-matrix in terms of tree-level data.
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