SU(2) WZW THEORIES WITH HERMITIAN PERTURBATIONS

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Abstract
We show the existence of higher order conserved quantities of isospin 1 (with spin 0,2,4,6,…) and isospin 0,2 (with spin 1,3,5,7,…) for the k=2 SU(2) WZW theory perturbed by the singlet combination of the isospin 1 primary field. We also show the possible existence of conserved isospin 0 current with spin 3 in the k→∞ limit. We also analyze these theories for finite k(≥3) and show that at least by counting arguments there exist no higher conserved quantities in these cases.

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