Quantum boundary currents for nonsimply-laced Toda theories

TL;DR

This paper investigates the quantum integrability of nonsimply-laced affine Toda theories on the half-plane, highlighting the importance of boundary terms for conserved higher-spin charges, which differ from classical expectations.

Contribution

It explicitly constructs higher-spin charges in nonsimply-laced affine Toda theories and reveals the significance of boundary total derivative terms in quantum conservation laws.

Findings

Higher-spin charges are explicitly constructed.

Boundary total derivative terms are crucial for quantum conservation.

Quantum boundary conservation differs from classical predictions.

Abstract

We study the quantum integrability of nonsimply--laced affine Toda theories defined on the half--plane and explicitly construct the first nontrivial higher--spin charges in specific examples. We find that, in contradistinction to the classical case, addition of total derivative terms to the "bulk" current plays a relevant role for the quantum boundary conservation.