We investigate the gauging of a $\mathbb{Z}_N$ 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 $\mathbb{Z}_N$ 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 $\mathbb{Z}_N$ 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 $\mathbb{Z}_N$ symmetry.We investigate the gauging of a $\mathbb{Z}_N$ 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 $\mathbb{Z}_N$ 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 $\mathbb{Z}_N$ 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 $\mathbb{Z}_N$ symmetry.

arXiv:2503.21524Mar 27, 20250 citations

Gauging ℤN symmetries of Narain CFTs

Keiichi Ando, Kohki Kawabata, 辰磨西岡

A bstract We investigate the gauging of a ℤ N 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 ℤ N 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 N 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 N symmetry.A bstract We investigate the gauging of a ℤ N 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 ℤ N 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 N 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 N symmetry.

Journal of High Energy PhysicsFeb 4, 20260 citations

Lattice bosonization

Maxime Kudinov, Peter Orland A. B. C

arXiv:hep-th/9601060Physics Letters BSep 1, 19960 citations

Gauging

\mathbb{Z}_N

symmetries of Narain CFTs

We investigate the gauging of a

\mathbb{Z}_N

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

\mathbb{Z}_N

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

\mathbb{Z}_N

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

\mathbb{Z}_N

symmetry.