Understanding NonInvertible Symmetries in Higher Dimensions Using Topological Defects
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Noninvertible topological defects in 4dimensional ℤ_{2} pure lattice gauge theory
(The 29th Outstanding Paper Award of the Physical Society of Japan)
Prog. Theor. Exp. Phys. 2022, 013B03 (2022).
By constructing KramersWannierWegner duality and Z_{2} duality defects and deriving their crossing relations, this study presents the first examples of codimension one noninvertible symmetries in fourdimensional 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 noninvertible 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 noninvertible 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 noninvertible symmetries in four dimensions (4D) using this approach.
Specifically, the researchers constructed topological defects associated with the KramersWannierWegner (KWW) duality in the 4D pure Z_{2} lattice gauge theory, similar to those in the twodimensional Ising model. They discovered that these defects were noninvertible. Additionally, they constructed Z_{2} 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 noninvertible symmetries in fourdimensional theories, this study was honored with the Outstanding Paper Award by the Physical Society of Japan. It marks a significant step towards understanding higherdimensional noninvertible symmetries and the fundamental nature of the universe.
Noninvertible topological defects in 4dimensional ℤ_{2} pure lattice gauge theory
(The 29th Outstanding Paper Award of the Physical Society of Japan)
Prog. Theor. Exp. Phys. 2022, 013B03 (2022).
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