Gapless phases in (2+1)d with non-invertible symmetries
- 1University of Oxford
- 2Rudolf Peierls Centre for Theoretical Physics
- 3University of Southern Denmark
Abstract
The study of gapless phases with categorical (or so-called non-invertible) symmetries is a formidable task, in particular in higher than two space-time dimensions. In this paper we build on previous works [L. Bhardwaj et al. SciPost Phys. 19, 056 (2025); L. Bhardwaj et al. arXiv:2502.20440] on gapped phases in (2+1)d and provide a systematic framework to study phase transitions with categorical symmetries. The Symmetry Topological Field Theory (SymTFT) is, as often in these matters, the central tool. Applied to gapless theories, we need to consider the extension of the SymTFT to interfaces between topological orders, so-called “club sandwiches”, which realize generalizations of so-called Kennedy-Tasaki (KT) transformations. This requires an input phase transition for a smaller symmetry, such as the Ising transition for \mathbb{Z}_2 ℤ 2 , and the SymTFT constructs a transformation to a gapless phase with a larger categorical symmetry. We carry this out for categorical symmetries whose SymTFT is a (3+1)d Dijkgraaf-Witten (DW) theory for a finite group G G with twist - so-called all bosonic fusion 2-categories. We classify such interfaces using a physically motivated picture of generalized gauging, as well as with a complementary analysis using (bi-)module 2-categories. This is exemplified in numerous Abelian and non-Abelian DW theories, giving rise to interesting gapless phases such as intrinsically gapless symmetry protected phases (igSPTs) and spontaneous symmetry breaking phases (igSSBs) from Abelian, S_3 S 3 , and D_8 D 8 DW theories.
Related
- Lattice models for phases and transitions with non-invertible symmetries
- Gauging on the lattice and gapped/gapless topological phases
- More about modular symmetries and non-invertible properties in magnetized compactifications
- Non-invertible symmetries and modular invariance in lattice models
- Non-invertible symmetries in the axiverse, and the imaginary wormholes
BibTeX
@article{bhardwaj2026gapless,
title = {{Gapless phases in (2+1)d with non-invertible symmetries}},
author = {Lakshya Bhardwaj and Yuhan Gai and Sheng-Jie Huang and Kansei Inamura and Sakura Schäfer‐Nameki and Apoorv Tiwari and Alison Warman},
journal = {SciPost Physics},
year = {2026},
month = jul,
doi = {10.21468/scipostphys.21.1.019},
url = {https://doi.org/10.21468/scipostphys.21.1.019},
note = {CC BY},
}
RIS
TY - JOUR
TI - Gapless phases in (2+1)d with non-invertible symmetries
AU - Lakshya Bhardwaj
AU - Yuhan Gai
AU - Sheng-Jie Huang
AU - Kansei Inamura
AU - Sakura Schäfer‐Nameki
AU - Apoorv Tiwari
AU - Alison Warman
PY - 2026
DA - 2026/07/23
JO - SciPost Physics
DO - 10.21468/scipostphys.21.1.019
UR - https://doi.org/10.21468/scipostphys.21.1.019
AB - The study of gapless phases with categorical (or so-called non-invertible) symmetries is a formidable task, in particular in higher than two space-time dimensions. In this paper we build on previous works [L. Bhardwaj et al. SciPost Phys. 19, 056 (2025); L. Bhardwaj et al. arXiv:2502.20440] on gapped phases in (2+1)d and provide a systematic framework to study phase transitions with categorical symmetries. The Symmetry Topological Field Theory (SymTFT) is, as often in these matters, the central tool. Applied to gapless theories, we need to consider the extension of the SymTFT to interfaces between topological orders, so-called “club sandwiches”, which realize generalizations of so-called Kennedy-Tasaki (KT) transformations. This requires an input phase transition for a smaller symmetry, such as the Ising transition for \mathbb{Z}_2 ℤ 2 , and the SymTFT constructs a transformation to a gapless phase with a larger categorical symmetry. We carry this out for categorical symmetries whose SymTFT is a (3+1)d Dijkgraaf-Witten (DW) theory for a finite group G G with twist - so-called all bosonic fusion 2-categories. We classify such interfaces using a physically motivated picture of generalized gauging, as well as with a complementary analysis using (bi-)module 2-categories. This is exemplified in numerous Abelian and non-Abelian DW theories, giving rise to interesting gapless phases such as intrinsically gapless symmetry protected phases (igSPTs) and spontaneous symmetry breaking phases (igSSBs) from Abelian, S_3 S 3 , and D_8 D 8 DW theories.
SN - 2542-4653
ER -