Understanding Non-Invertible Symmetries in Higher Dimensions Using Topological Defects


2024-9-27

JPS Hot Topics 4, 030

https://doi.org/10.7566/JPSHT.4.030

© The Physical Society of Japan

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Non-invertible topological defects in 4-dimensional ℤ2 pure lattice gauge theory
(The 29th Outstanding Paper Award of the Physical Society of Japan)

Masataka Koide, Yuta Nagoya, and Satoshi Yamaguchi
Prog. Theor. Exp. Phys. 2022, 013B03 (2022).

By constructing Kramers-Wannier-Wegner duality and Z2 duality defects and deriving their crossing relations, this study presents the first examples of codimension one non-invertible symmetries in four-dimensional quantum field theories.


Symmetry is a fundamental concept of physics that describes how the laws of physics remain unchanged under certain transformations. Generalized symmetries are an extension of this concept, which, in recent times, has been applied to the analysis of quantum field theories. Among these are non-invertible symmetries which do not have inverse elements and cannot be undone, unlike traditional symmetries. However, they are less understood in higher dimensions than in two dimensions.

Generalized symmetries have been discovered by identifying the relations between symmetries and topological defects. These defects are like disruptions or “wrinkles” in the fabric of a physical system. They cannot be removed or smoothed out easily without creating a defect elsewhere. An interesting approach to understanding non-invertible symmetries is to construct topological defects.

Now, in a new study published in the Progress of Theoretical and Experimental Physics, researchers have, for the first time, presented concrete examples of non-invertible symmetries in four dimensions (4D) using this approach.

Specifically, the researchers constructed topological defects associated with the Kramers-Wannier-Wegner (KWW) duality in the 4D pure Z2 lattice gauge theory, similar to those in the two-dimensional Ising model. They discovered that these defects were non-invertible. Additionally, they constructed Z2 symmetry defects as well as defect junctions between these defects and the KWW duality defects. They derived the crossing relations and using these, calculated the expectation values for some of the defects.

Having accelerated the study of non-invertible symmetries in four-dimensional theories, this study was honored with the Outstanding Paper Award by the Physical Society of Japan. It marks a significant step towards understanding higher-dimensional non-invertible symmetries and the fundamental nature of the universe.

Non-invertible topological defects in 4-dimensional ℤ2 pure lattice gauge theory
(The 29th Outstanding Paper Award of the Physical Society of Japan)

Masataka Koide, Yuta Nagoya, and Satoshi Yamaguchi
Prog. Theor. Exp. Phys. 2022, 013B03 (2022).

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