What type of study is this?

This is a Quantitative Study study.

October 8, 2025Open Access

Higher symmetries, anomalies, and crossed squares in lattice gauge theory

Key Points

The study demonstrates that both higher-form symmetries and 't Hooft anomalies stem from symmetry restrictions in spatial regions.
Important findings show that the data of symmetry transformations can be represented as a higher group structure.
By focusing on two spatial dimensions, the research illustrates how crossed squares model components of gauge theory.
The implications extend to proposing that higher groups manifest as crossed n-cubes in various models and quantum field theories.

Abstract

We examine higher-form symmetries of quantum lattice gauge theories through the lens of homotopy theory and operator algebras. We show that in the operator-algebraic approach both higher-form symmetries and 't Hooft anomalies arise from considering restrictions of symmetry transformations to spatial regions. The data of these restrictions are naturally packaged into a higher group. For example, for gauge theories in two spatial dimensions, this information is encoded in a crossed square of groups, which is an algebraic model of a 3-group. In general, we propose that higher groups appear in lattice models and QFT as crossed n-cubes of groups via a nonabelian version of the Cech construction.

Higher symmetries, anomalies, and crossed squares in lattice gauge theory

Key Points

Abstract

Cite This Study

Also Consider

Also Consider