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arXiv · 2603.03438

On the action of non-invertible symmetries on local operators in 3+1d

Pavel Putrov·Rajath Radhakrishnan
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Abstract

Most of the known non-invertible symmetries of quantum field theories in three and four spacetime dimensions act invertibly on local operators. An exception is coset symmetries, which can be constructed from gauging a non-normal subgroup of an invertible symmetry. In this paper, we study the action of a general finite non-invertible symmetry on local operators in four dimensions. We show that non-invertible symmetries without topological line operators necessarily act invertibly on local operators. Using this result, we argue that the action of a general non-invertible symmetry in 3+1d on local operators can be decomposed into the invertible action of some operators composed with the action of a gauging interface. We use this result to study when such a symmetry is anomaly-free. We find a necessary condition for a finite non-invertible symmetry in 3+1d to be anomaly-free, and show that anomaly-free non-invertible symmetries without topological line operators are non-intrinsically non-invertible.

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Pavel Putrov, Rajath Radhakrishnan. 2026-03-03. On the action of non-invertible symmetries on local operators in 3+1d. https://arxiv.org/abs/2603.03438

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