Quantum, higher-spin, local charges in symmetric space sigma models

Abstract

Potential anomalies are analysed for the local spin-3 and spin-4 classically conserved currents in any two-dimensional sigma model on a compact symmetric space $G/H$, with $G$ and $H$ classical groups. Quantum local conserved charges are shown to exist in exactly those models which also possess quantum non-local (Yangian) charges. The possibility of larger sets of quantum local charges is discussed and shown to be consistent with known S-matrix results and the behaviour of the corresponding Yangian representations.

v2: 17 pages; refs added

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• Higher-spin conserved currents in supersymmetric sigma models on symmetric spaces
• An Index for Quantum Integrability
• Lax pair and Darboux transformation of noncommutative U(N) principal chiral model
• Spectra of Coset Sigma Models
• Pseudoduality Between Symmetric Space Sigma Models
• Dorey's Rule and the q-Characters of Simply-Laced Quantum Affine Algebras
• Conserved Charges in the Principal Chiral Model on a Supergroup
• Superfield Lax formalism of supersymmetric sigma model on symmetric spaces
• Special Holonomy and Two-Dimensional Supersymmetric Sigma-Models
• On higher spin symmetries in de Sitter QFTs
• Notes on index of quantum integrability