Four-dimensional Wess--Zumino--Witten actions (Q1400165)

The author presents an axiomatic construction of the Wess-Zumino-Witten action (WZW actions) valued in \(G= \text{SU}(N)\), \(N\geq 3\). This construction is realized as a functor WZ from the category of conformally flat four-manifolds to the category of line bundles that satisfies, besides the axioms of a topological field theory, the axioms which abstract the characteristics of WZW actions. He describes the conformally flat manifolds, the four-dimensional WZW model and studies some properties of the line bundles on \(\Omega^3G\). Next he presents the construction of WZW actions, by constructing the line bundle \(\text{WZ}(F)\) and obtaining the Polyakov-Wiegmann formula. Finally, the author obtains the extensions of the group \(\Omega^3_0 G\).