Beschreibung
Beyond Chern-Simons: The Algebraic Topology of Superconformal Anomalies
Abstract: We present a unified BRST-cohomological framework for anomalies, extending the Chern-Simons formulation of Yang–Mills anomalies to encompass all four-dimensional superconformal anomalies. Central to our approach is the characterization of anomalies through the constraint ideal in the polynomial ring formed from generalized curvatures and connections of the underlying symmetry (super)-Lie algebra. In Yang–Mills theory, the constraint ideal is generated solely by curvatures, so anomalies correspond to invariant Chern curvature polynomials. In contrast, the constraint ideal for four-dimensional (super)conformal gravity includes additional polynomials that mix curvatures and connections. This enriched structure naturally explains the coexistence of both Chern-type (a) and non-Chern-type (c) anomalies in (super)conformal theories.