Holonomy and the Wess-Zumino term
If M is a manifold, Z a \((d-1)\)-dimensional manifold, and \(h\in C^{\infty}(S^ 1\times Z,M)\), the Wess-Zumino term \(\Gamma_{wz}(h)\) of h is defined by \(\Gamma_{wz}(h)=\exp \int_{H(D\times Z)}\omega\), where \(\omega/2\pi i\) is any integral closed \((d+1)\)-form, and \(H: D\times Z\to M\) is any smooth extension of h (D the unit disc). The authors show that the Wess-Zumino term of h can be interpreted as a holonomy term, i.e. the holonomy of some suitable curvature 2-form on \(C^{\infty}(Z,M)\) along \(\hat h:\) \(S^ 1\to C^{\infty}(Z,M)\), where \(\hat h(\theta)\)(z)\(=h(\theta,z)\).
scientific article; zbMATH DE number 4011488