Four-dimensional Wess–Zumino–Witten actions

✍ Scribed by Tosiaki Kori

• Book ID: 104343198
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 196 KB
• Volume: 47
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(02)00220-6

✦ Synopsis

We shall give an axiomatic construction of Wess-Zumino-Witten (WZW) actions valued in G = SU(N), N ≥ 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 that satisfies, besides the axioms of a topological field theory, the axioms which abstract the characteristics of WZW actions. To each conformally flat four-dimensional manifold Σ with boundary Γ = ∂Σ, a line bundle L = WZ(Γ) with connection over the space ΓG of mappings from Γ to G is associated. The WZW action is a non-vanishing horizontal section WZ(Σ) of the pullback bundle r * L over ΣG by the boundary restriction r : ΣG → ΓG. WZ(Σ) is required to satisfy a generalized Polyakov-Wiegmann formula with respect to the pointwise multiplication of the fields ΣG. Associated to the WZW action there is a geometric description of the extension of the Lie group Ω 3 G due to Mickelsson. In fact, we have two Abelian extensions of Ω 3 G that are in duality.