Quantum conserved currents in affine Toda theories

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 correspondinh 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.