Non-local charges and quantum integrability of sigma models on the symmetric spaces SO(2n)/SO(n)xSO(n) and Sp(2n)/Sp(n)xSp(n)

TL;DR

This paper demonstrates that certain two-dimensional sigma models with specific symmetric space targets possess non-local and local conserved charges that remain intact after quantization, confirming their quantum integrability.

Contribution

It proves the quantum survival of non-local charges in these sigma models and shows local higher-spin charges survive in the SO(2n)/SO(n) models, establishing their integrability at the quantum level.

Findings

Non-local conserved charges persist after quantization.

Local higher-spin charges survive in SO(2n)/SO(n) models.

The models are confirmed to be integrable quantum mechanically.

Abstract

Non-local conserved charges in two-dimensional sigma models with target spaces $SO(2n)/SO(n){\times}SO(n)$ and $Sp(2n)/Sp(n){\times}Sp(n)$ are shown to survive quantization, unspoiled by anomalies; these theories are therefore integrable at the quantum level. Local, higher-spin, conserved charges are also shown to survive quantization in the $SO(2n)/SO(n){\times}SO(n)$ models.