On the 2D Zero Modes’ Algebra of the SU(n) WZNW Model

Abstract

AbstractA quantum group covariant extension of the chiral parts of the Wess-Zumino-Novikov-Witten (WZNW) model on a compact Lie group G gives rise to two matrix algebras with non-commutative entries. These are generated by “chiral zero modes” \(a_{\alpha }^{i}\,,\bar{a}_{j}^{\beta }\) which combine, in the 2D model, into \(Q_{j}^{i} = a_{\alpha }^{i} \otimes \bar{ a}_{j}^{\alpha }\). The Q-operators provide important information about the internal symmetry and the fusion ring. Here we review earlier results about the SU(n) WZNW Q-algebra and its Fock representation for n = 2 and make the first steps towards their generalization to n ≥ 3.KeywordsZero ModeWZNW ModelChiral Zero ModesChiral PartRing FusionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.