• Corpus ID: 253761101

# 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}
}
• Published 21 November 2022
• Mathematics
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

## Figures from this paper

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
• 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
• 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
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
• 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
• Physics
• 2022
We study the boundary states of the archetypal three dimensional topological order, i.e

## References

SHOWING 1-10 OF 137 REFERENCES

• Physics
SciPost 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
• 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
• 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
• Mathematics
Journal 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
• Physics
Journal 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
• 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
• 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
• Physics
Journal 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
• 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
• 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