Quantum Conserved Currents in Affine Toda Theories

TL;DR

This paper investigates the quantum conservation of higher-spin currents in affine Toda theories, demonstrating all-loop conservation in specific cases and analyzing anomalies affecting charge conservation and bootstrap methods.

Contribution

It proves all-loop conservation of certain higher-spin currents in affine Toda theories and examines quantum anomalies impacting charge conservation and S-matrix bootstrap procedures.

Findings

All-loop conservation of spin-3 currents in specific affine Toda theories.

One-loop corrections to higher-spin charges are computed.

Anomalous threshold singularities can break charge conservation.

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.