Journal of High Energy Physics· 2018Q2
On finite symmetries and their gauging in two dimensions
- 300citations
- Q2SCImago
- 2018year
Short summary
Researchers generalized the concept of gauging symmetries from groups to unitary fusion categories, revealing dual symmetries and enabling the study of non-Abelian symmetries arising from Abelian ones.
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Key points
- Gauging a ℤn symmetry in 2D yields a dual ℤn symmetry, a concept generalized to non-Abelian groups.
- Symmetries are redefined using unitary fusion categories, allowing for broader applications than group-based definitions.
- The framework explains how gauging subgroups of anomalous finite groups can generate non-Abelian symmetries from Abelian ones.
- The gauged theory is shown to be a topological quantum field theory with a new symmetry given by a dual category.
AI-generated from the title and abstract; the full text is not read.
Abstract
A bstract It is well-known that if we gauge a ℤ n symmetry in two dimensions, a dual ℤ n symmetry appears, such that re-gauging this dual ℤ n symmetry leads back to the original theory. We describe how this can be generalized to non-Abelian groups, by enlarging the concept of symmetries from those defined by groups to those defined by unitary fusion categories. We will see that this generalization is also useful when studying what happens when a non-anomalous subgroup of an anomalous finite group is gauged: for example, the gauged theory can have non-Abelian group symmetry even when the original symmetry is an Abelian group. We then discuss the axiomatization of two-dimensional topological quantum field theories whose symmetry is given by a category. We see explicitly that the gauged version is a topological quantum field theory with a new symmetry given by a dual category.
The authors' abstract, as published at the source. Journal of High Energy Physics, 2018 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics