Geometry and anomaly structure of supersymmetric \(\sigma\)-models
Supersymmetric \(\sigma\)-models, which describe low-energy interactions of Goldstone fields arising from spontaneous symmetry breaking, correspond to non-compact, non-homogeneous Kähler manifolds. We discuss systematically general features of this class of \(\sigma\)-models in comparison with the more familiar \(\sigma\)-models based on compact, homogeneous (coset) Kähler manifolds \(G/H\). A key property of supersymmetric \(\sigma\)-models is their hidden invariance under local \(\tilde H\) transformations, where \(\tilde H\) is a subgroup of the complexificaton \(\bar G\) of G, which characterizes the specific model. Contrary to homogeneous ones, non-homogeneous \(\sigma\)-models may be supplemented with local counter terms which cancel isometry anomalies. We illustrate our general discussion by means of a \(\sigma\)-model based on the coset space \(U(n+2)/U(n)\times SU(2).\)
scientific article; zbMATH DE number 4007204