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.
q-deformed Coxeter element in Non-simply-laced Affine Toda Field Theories
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abstract
The Lie algebraic structures of the S-matrices for the affine Toda field theories based on the dual pairs (X_N^{(1)}, Y_M^{(l)}) are discussed. For the non-simply-laced horizontal subalgebra X_N and the simply-laced horizontal subalgebra Y_M, we introduce a ``q-deformation'' of a Coxeter element and a ``p-deformation'' of a twisted Coxeter element respectively. Using these deformed objects, expressions for the generating function of the multiplicities of the building block of the S-matrices are obtained. The relation between the deformed version of Dorey's rule and generalized Dorey's rule due to Chari and Pressley are discussed.
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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.