Anomalies of non-invertible self-duality symmetries: fractionalization and gauging"

Abstract: Anomalies of global symmetries are important tools for constraining the dynamics of QFTs, hence their generalization to non-invertible symmetries is clearly important. Their definition and classification, however, are still puzzling. In this talk, I will argue that defining anomalies as obstructions to gauging makes them computable using symmetry topological field theory (SymmTFT). I will focus on duality defects, arising in d=2n dimensional theories self-dual under gauging a finite abelian n-1 form symmetry. For d=2, the classification of anomalies was already known in the mathematical literature, and I will demonstrate how to reproduce these results with techniques easily generalizable to higher dimensions. In any dimension, we find two obstructions to gauging. The first indicates that intrinsically non-invertible symmetries are always anomalous. When this obstruction vanishes, a second one can emerge, linked to a pure anomaly in the global variant where the duality defect is invertible. Calculating this requires extra data, which I will argue corresponds to a choice of symmetry fractionalization. Based on joint work (2308.11707) with F. Benini, C. Copetti, G. Galati, G. Rizi.

HEP - phenomenologyHEP - theorymathematical physicscategory theory

Audience: researchers in the topic

Symmetry Seminar

Series comments: Weekly seminar on generalized symmetries in QFT, string theory and related topics.