Gauging Non-Invertible Symmetries in (2+1)d Topological Orders
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909671720222720 |
|---|---|
| author | Balasubramanian, Mahesh K. N. Buican, Matthew Delcamp, Clement Radhakrishnan, Rajath |
| author_facet | Balasubramanian, Mahesh K. N. Buican, Matthew Delcamp, Clement Radhakrishnan, Rajath |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gauging Non-Invertible Symmetries in (2+1)d Topological Orders Balasubramanian, Mahesh K. N. Buican, Matthew Delcamp, Clement Radhakrishnan, Rajath High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Physics 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. |
| title | Gauging Non-Invertible Symmetries in (2+1)d Topological Orders |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2507.01142 |