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A systematic description of the Wess-Zumino-Witten model is presented. The symplectic method plays the major role in this paper and also gives the relationship between the WZW model and the Chern-Simons model. The quantum theory is obtained to give the projective representation of the Loop group. The Gauss constraints for the connection whose curvature is only focused on several fixed points are solved. The Kohno connection and the Knizhnik-Zamolodchikov equation are derived. The holonomy representation and $check R$-matrix representation of braid group are discussed.
We revisit various topological issues concerning four-dimensional ungauged and gauged Wess-Zumino-Witten (WZW) terms for $SU$ and $SO$ quantum chromodynamics (QCD), from the modern bordism point of view. We explain, for example, why the definition of
We shall give an axiomatic construction of Wess-Zumino-Witten actions valued in (G=SU(N)), (Ngeq 3). It is realized as a functor ({WZ}) from the category of conformally flat four-dimensional manifolds to the category of line bundles with connection t
We continue the study of the gl(1|1) Wess-Zumino-Witten model. The Knizhnik-Zamolodchikov equations for the one, two, three and four point functions are analyzed, for vertex operators corresponding to typical and projective representations. We illust
One loop anomalies and their dependence on antifields for general gauge theories are investigated within a Pauli-Villars regularization scheme. For on-shell theories {it i.e.}, with open algebras or on-shell reducible theories, the antifield dependen
We consider the problem of the decomposition of the Renyi entanglement entropies in theories with a non-abelian symmetry by doing a thorough analysis of Wess-Zumino-Witten (WZW) models. We first consider $SU(2)_k$ as a case study and then generalise