Work

Difference between pair creation and anomaly matching: Nontrivial aspects of invertible symmetries and defects in $SU(N)$ models

Year: 2026

Type: preprint

Abstract: We study the connection between the $SU(N)_{K}$ Wess-Zumino-Witten (WZW) model and $SU(N)_{K'}$ WZW model, enforcing the $\mathbb{Z}_{N}$ symmetries. The fundamental underlying structures are the (half-)integer spin simple currents in the topological quantum field theories and anomaly matching conditions in conformal field theories. For the (half-)integer spin simple current condition, we obtain the generalized pairing condition $K= \pm R^{2}K' (\text{mod}.N)$ with $\text{gcd}(R,N)=1$. On the other hand, the anomaly matching condition results in the weaker condition $K= \pm RUK' (\text{mod}.N)$ with $\text{gcd}(R,N)=\text{gcd}(U,N)=1$. The preservation law of the $\mathbb{Z}_{N}$ defects and symmetries is compatible only with the pairing condition.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.21478

Authors: Fukusumi, Yoshiki, Nakashiba, Shuma

Institutions: National Taiwan University, National Center for Theoretical Sciences, National Center for Theoretical Sciences, Physics Division, The Institute for Solid State Physics, The University of Tokyo, The University of Tokyo

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Center for Theoretical Sciences

OpenAlex ID: W7222405067

Cites: 93

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Related to: 10