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<p>We investigate the gauging of a ℤ<sub><i>N</i></sub> symmetry in lattice conformal field theories (CFTs), also known as Narain CFTs. For prime <i>N</i>, we derive a spin selection rule for operators in a ℤ<sub><i>N</i></sub> charge-twisted sector of a general bosonic CFT. Using this result, we formulate the gauging procedures in lattice CFTs as modifications of the momentum lattices by a lattice vector that specifies a non-anomalous ℤ<sub><i>N</i></sub> symmetry. Applying this formulation to code CFTs, i.e., Narain CFTs constructed from error-correcting codes, we express the torus partition functions of the orbifolded and parafermionized theories in terms of the weight enumerator polynomials of the underlying codes. As an application, we identify a class of codes that yield self-dual bosonic CFTs under the orbifolding by a ℤ<sub><i>N</i></sub> symmetry.</p>

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Gauging ℤN symmetries of Narain CFTs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月4日

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  • Keiichi Ando,
  • Kohki Kawabata,
  • Tatsuma Nishioka

摘要

We investigate the gauging of a ℤN symmetry in lattice conformal field theories (CFTs), also known as Narain CFTs. For prime N, we derive a spin selection rule for operators in a ℤN charge-twisted sector of a general bosonic CFT. Using this result, we formulate the gauging procedures in lattice CFTs as modifications of the momentum lattices by a lattice vector that specifies a non-anomalous ℤN symmetry. Applying this formulation to code CFTs, i.e., Narain CFTs constructed from error-correcting codes, we express the torus partition functions of the orbifolded and parafermionized theories in terms of the weight enumerator polynomials of the underlying codes. As an application, we identify a class of codes that yield self-dual bosonic CFTs under the orbifolding by a ℤN symmetry.