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.
A remark on the coupling-dependence in affine Toda field theories
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abstract
The affine Toda field theories based on the non simply-laced Lie algebras are discussed. By rewriting the S-matrix formulae found by Delius et al, a universal form for the coupling-constant dependence of these models is obtained, and related to various general properties of the classical couplings. This is illustrated via the S-matrix associated with the dual pair of algebras $f_4^{(1)}$ and $e_6^{(2)}$.
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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.