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arXiv · 2308.11707

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

Andrea Antinucci·Francesco Benini·Christian Copetti·Giovanni Galati·Giovanni Rizi
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Abstract

We study anomalies of non-invertible duality symmetries in both 2d and 4d, employing the tool of the Symmetry TFT. In the 2d case we rephrase the known obstruction theory for the Tambara-Yamagami fusion category in a way easily generalizable to higher dimensions. In both cases we find two obstructions to gauging duality defects. The first obstruction requires the existence of a duality-invariant Lagrangian algebra in a certain Dijkgraaf-Witten theory in one dimension more. In particular, intrinsically non-invertible (a.k.a. group theoretical) duality symmetries are necessarily anomalous. The second obstruction requires the vanishing of a pure anomaly for the invertible duality symmetry. This however depends on further data. In 2d this is specified by a choice of equivariantization for the duality-invariant Lagrangian algebra. We propose and verify that this is equivalent to a choice of symmetry fractionalization for the invertible duality symmetry. The latter formulation has a natural generalization to 4d and allows us to give a compact characterization of the anomaly. We comment on various possible applications of our results to self-dual theories.

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Andrea Antinucci, Francesco Benini, Christian Copetti, Giovanni Galati, Giovanni Rizi. 2023-08-22. Anomalies of non-invertible self-duality symmetries: fractionalization and gauging. https://arxiv.org/abs/2308.11707

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