Conserved Charges and Supersymmetry in Principal Chiral Models

Abstract

We report on investigations of local (and non-local) charges in bosonic and supersymmetric principal chiral models in 1+1 dimensions. In the bosonic PCM there is a classically conserved local charge for each symmetric invariant tensor of the underlying group. These all commute with the non-local Yangian charges. The algebra of the local charges amongst themselves is rather more subtle. We give a universal formula for infinite sets of mutually commuting local charges with spins equal to the exponents of the underlying classical algebra modulo its Coxeter number. Many of these results extend to the supersymmetric PCM, but with local conserved charges associated with antisymmetric invariants in the Lie algebra. We comment briefly on the quantum conservation of local charges in both the bosonic and super PCMs.

18 pages, LaTeX. Revised and up-dated version based on conference talks by JME and NJM

References in corpus (6)

• Deformations of W-algebras associated to simple Lie algebras
• Yangians, Integrable Quantum Systems and Dorey's rule
• The full set of $c_n$-invariant factorized $S$-matrices
• Hidden geometrical structures in integrable models
• Algebra of Non-Local Charges in Supersymmetric Non-Linear Sigma Models
• Lattice quantization of Yangian charges

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• The SO(N) principal chiral field on a half-line
• Quantum Integrability of Coupled N=1 Super Sine/Sinh-Gordon Theories and the Lie Superalgebra D(2,1;\A)
• Quantum affine Toda solitons