2025/07/22 by Camillo Imbimbo, Imbimbo, Camillo, Ludovico Porro +1
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #Distributed and Parallel Computing Systems #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.2507.16505
openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a unified topological description of anomalies that generalizes the Chern-Simons formulation of Yang-Mills anomalies to encompass all 4-dimensional superconformal anomalies. The key innovation is our characterization of anomalies through the constraint ideal in the polynomial ring of generalized curvatures and connections of the underlying symmetry (super)-Lie algebra. We demonstrate that anomalies in dimension d are captured by the cohomology Hδ(Wd+2) of the generalized BRST operator δ acting on the fermion number d+2 component of the constraint ideal Wd+2. While Yang-Mills anomalies correspond to invariant Chern curvature polynomials (where Wd+2 reduces to homogeneous curvature polynomials), the constraint ideal for 4D (super)conformal gravity contains additional polynomials mixing curvatures and connections. This richer structure naturally explains the coexistence of both Chern-type (a) and non-Chern-type (c) anomalies in (super)conformal theories.