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<p>Duality symmetries have been extensively investigated in various contexts, playing a crucial role in understanding quantum field theory and condensed matter theory. In this paper, we extend this framework by studying <i>N</i> -ality symmetries, which are a generalization of duality symmetries and are mathematically described by ℤ<sub><i>N</i></sub> -graded fusion categories. In particular, we focus on an <i>N</i> -ality symmetry obtained by gauging a non-anomalous subgroup of ℤ<sub><i>N</i></sub> × ℤ<sub><i>N</i></sub> × ℤ<sub><i>N</i></sub> symmetry with a type III anomaly. We determine the corresponding fusion rules via two complementary approaches: a direct calculation and a representation-theoretic method. As an application, we study the symmetry-protected topological (SPT) phases associated with the <i>N</i> -ality symmetry. We classify all such SPT phases using the SymTFT framework and explicitly construct lattice Hamiltonians for some of them.</p>

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N-ality symmetry and SPT phases in (1+1)d

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  • 发表日期：

    2025年12月10日

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  • Jun Maeda,
  • Tsubasa Oishi

摘要

Duality symmetries have been extensively investigated in various contexts, playing a crucial role in understanding quantum field theory and condensed matter theory. In this paper, we extend this framework by studying N -ality symmetries, which are a generalization of duality symmetries and are mathematically described by ℤN -graded fusion categories. In particular, we focus on an N -ality symmetry obtained by gauging a non-anomalous subgroup of ℤN × ℤN × ℤN symmetry with a type III anomaly. We determine the corresponding fusion rules via two complementary approaches: a direct calculation and a representation-theoretic method. As an application, we study the symmetry-protected topological (SPT) phases associated with the N -ality symmetry. We classify all such SPT phases using the SymTFT framework and explicitly construct lattice Hamiltonians for some of them.