Gauging Non-Invertible Symmetries in (2+1)d Topological Orders

• URL: http://arxiv.org/abs/2507.01142v1
• Date: Tue, 01 Jul 2025 19:00:39 GMT
• Title: Gauging Non-Invertible Symmetries in (2+1)d Topological Orders
• Authors: Mahesh K. N. Balasubramanian, Matthew Buican, Clement Delcamp, Rajath Radhakrishnan,
• Abstract summary: We present practical and formal methods for gauging non-invertible symmetries in (2+1)d quantum field theories.<n>We generalize various aspects of invertible 0-form gauging, including symmetry fractionalization, discrete torsion, and the fixed point theorem for symmetry action on lines.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present practical and formal methods for gauging non-invertible symmetries in (2+1)d topological quantum field theories. Along the way, we generalize various aspects of invertible 0-form gauging, including symmetry fractionalization, discrete torsion, and the fixed point theorem for symmetry action on lines. Our approach involves two complementary strands: the fusion of topological interfaces and Morita theory of fusion 2-categories. We use these methods to derive constraints on gaugeable symmetries and their duals while unifying the prescription for gauging non-invertible 0-form and 1-form symmetries and various higher structures. With a view toward recent advances in creating non-Abelian topological orders from Abelian ones, we give a simple recipe for non-invertible 0-form gauging that takes large classes of the latter to the former. We also describe conditions under which iterated gauging of invertible 0-form symmetries is equivalent to a single-step gauging of a non-invertible symmetry. We conclude with a set of concrete examples illustrating these various phenomena involving gauging symmetries of the infrared limit of the toric code.

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