Extended non-abelian gauge symmetries in the classical WZNW model

Non-Abelian Bosonization and Higher Spin Symmetries

“…However, as was shown in [17] (see also [22]) a class transformations exist for the case of the WZNW model in which terms violating the assertions ii) and iii) appear. The latter means that the current⇐⇒symmetry correspondence is not invertible in this case.…”

“…In paper [17] it was shown that these currents can be represented by the Faá di Bruno polynomials too, which show us that (3.19) is an appropriate bosonization of the higher spin fermionic currents (2.1). Indeed the currents (3.19) can be represented in the form: 20) where the notations…”

“…In order to assure that the currents (3.25b) have a Noether character we should introduce higher rank isotopic tensor currents (see [17] and [22]). …”

“…By means of this method in the papers [16] and [17] some difference between the symmetry properties of the classical free fermionic model and the classical WZNW model with respect to the higher spin transformations was obtained. Indeed, although the action integrals of both models are invariant with respect to the transformations satisfying isomorphic extended symmetry algebras; the DOP (S 1 )…”

“…transformations [18] - [20], the corresponding higher spin currents for both models have different properties [21], [16] and [17]. In the paper [19], [9], [21] it is shown that the higher spin fermionic currents satisfied a closed current algebra, which coincides with the algebra of the corresponding field transformations [16].…”