# Higher-group symmetry in finite gauge theory and stabilizer codes

@inproceedings{Barkeshli2022HighergroupSI, title={Higher-group symmetry in finite gauge theory and stabilizer codes}, author={Maissam Barkeshli and Yu-An Chen and Po-Shen Hsin and Ryohei Kobayashi}, year={2022} }

A large class of gapped phases of matter can be described by topological ﬁnite group gauge theories. In this paper, we derive the d -group global symmetry and its ’t Hooft anomaly for topological ﬁnite group gauge theories in ( d +1) space-time dimensions, including non-Abelian gauge groups and Dijkgraaf-Witten twists. We focus on the 1-form symmetry generated by invertible (Abelian) magnetic defects and the higher-form symmetries generated by invertible topological defects decorated with lower…

## 6 Citations

### Non-Invertible Defects in Nonlinear Sigma Models and Coupling to Topological Orders

- Physics
- 2022

Nonlinear sigma models appear in a wide variety of physics contexts, such as the long-range order with spontaneously broken continuous global symmetries. There are also large classes of quantum…

### Gapped boundary of (4+1)d beyond-cohomology bosonic SPT phase

- Mathematics, Physics
- 2023

In this work we study gapped boundary states of $\mathbb{Z}_N$ bosonic symmetry-protected topological (SPT) phases in 4+1d, which are characterized by mixed $\mathbb{Z}_N$-gravity response, and the…

### On Topology of the Moduli Space of Gapped Hamiltonians for Topological Phases

- Mathematics
- 2022

The moduli space of gapped Hamiltonians that are in the same topological phase is an intrinsic object that is associated to the topological order. The topology of these moduli spaces is used recently…

### Non-invertible symmetries in axion electrodynamics

- Physics, Mathematics
- 2022

We study non-invertible global symmetries in (3 + 1)-dimensional axion electrodynamics with a massless axion and a massless photon. In addition to a previously known non-invertible 0-form shift…

### Emergent higher-symmetry protected topological orders in the confined phase of $U(1)$ gauge theory

- Physics, Mathematics
- 2022

We consider compact $U^\kappa(1)$ gauge theory in 3+1D with the $2\pi$-quantized topological term ${\sum_{I, J =1}^\kappa\frac{K_{IJ}}{4\pi}\int_{M^4}F^I\wedge F^J}$. At energies below the gauge…

### Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point

- Physics
- 2022

We study the boundary states of the archetypal three dimensional topological order, i.e

## References

SHOWING 1-10 OF 137 REFERENCES

### Exotic invertible phases with higher-group symmetries

- PhysicsSciPost Physics
- 2022

We investigate a family of invertible phases of matter with
higher-dimensional exotic excitations in even spacetime dimensions,
which includes and generalizes the Kitaev’s chain in 1+1d. The…

### Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases

- Mathematics
- 2019

We study generalized discrete symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse. In particular, we describe 't Hooft anomalies and classify gapped…

### Symmetry protected topological orders and the group cohomology of their symmetry group

- Physics
- 2013

Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the…

### On 2-group global symmetries and their anomalies

- MathematicsJournal of High Energy Physics
- 2019

A bstractIn general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using…

### Symmetry-enriched quantum spin liquids in (3 + 1)d

- PhysicsJournal of High Energy Physics
- 2020

We use the intrinsic one-form and two-form global symmetries of (3+1)d bosonic field theories to classify quantum phases enriched by ordinary (0-form) global symmetry. Different symmetry-enriched…

### Symmetry-protected topological orders for interacting fermions: Fermionic topological nonlinear σ models and a special group supercohomology theory

- Physics
- 2014

Symmetry-protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry $G$, which can all be smoothly connected to the trivial product states if we break the…

### Higher symmetry and gapped phases of gauge theories

- Mathematics, Physics
- 2013

We study topological field theory describing gapped phases of gauge theories where the gauge symmetry is partially Higgsed and partially confined. The TQFT can be formulated both in the continuum and…

### Modified instanton sum in QCD and higher-groups

- PhysicsJournal of High Energy Physics
- 2020

We consider the SU( N ) Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of p . We can formulate such a quantum field theory maintaining…

### Anomaly Obstructions to Symmetry Preserving Gapped Phases

- Physics, Mathematics
- 2019

Anomalies are renormalization group invariants that constrain the dynamics of quantum field theories. We show that certain anomalies for discrete global symmetries imply that the underlying theory…

### Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions

- Mathematics
- 2022

We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of…