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Quantum Conserved Currents in Affine Toda Theories

G. W. Delius·M. T. Grisaru·D. Zanon
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Abstract

We study the renormalization and conservation at the quantum level of higher-spin currents in affine Toda theories with particular emphasis on the nonsimply-laced cases. For specific examples, namely the spin-3 current for the $a_3^{(2)}$ and $c_2^{(1)}$ theories, we prove conservation to all-loop order, thus establishing the existence of factorized S-matrices. For these theories, as well as the simply-laced $a_2^{(1)}$ theory, we compute one-loop corrections to the corresponding higher-spin charges and study charge conservation for the three-particle vertex function. For the $a_3^{(2)}$ theory we show that although the current is conserved, anomalous threshold singularities spoil the conservation of the corresponding charge for the on-shell vertex function, implying a breakdown of some of the bootstrap procedures commonly used in determining the exact S-matrix.

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G. W. Delius, M. T. Grisaru, D. Zanon. 1992-02-20. Quantum Conserved Currents in Affine Toda Theories. https://doi.org/10.1016/0550-3213(92)90103-i

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