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arXiv:2503.21524

Gauging $\mathbb{Z}_N$ symmetries of Narain CFTs

Ando, Keiichi, Kohki Kawabata, Tatsuma Nishioka

Published Mar 27, 2025• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2503.21524

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Gauging ZN\mathbb{Z}_NZN​ symmetries of Narain CFTs
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Narain CFTs from quantum codes and their Z2{\mathbb{Z}}_{2}Z2​ gauging
A bstract We investigate the gauging of a Z2{\mathbb{Z}}_{2}Z2​ symmetry in Narain conformal field theories (CFTs) constructed from qudit stabilizer codes. Considering both orbifold and fermionization, we establish a connection between Z2{\mathbb{Z}}_{2}Z2​ gauging procedures and modifications of the momentum lattice by vectors characterizing the Z2{\mathbb{Z}}_{2}Z2​ symmetry. We also provide three-dimensional interpretations of Z2{\mathbb{Z}}_{2}Z2​ gaugings through abelian Chern-Simons theories, which act as symmetry topological field theories.
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Topological phases of matter in (2+1) dimensions are commonly equipped with global symmetries, such as electric-magnetic duality in gauge theories and bilayer symmetry in fractional quantum Hall states. Gauging these symmetries into local dynamical ones is one way of obtaining exotic phases from conventional systems. We study this using the bulk-boundary correspondence and applying the orbifold construction to the (1+1)-dimensional edge described by a conformal field theory (CFT). Our procedure puts twisted boundary conditions into the partition function and predicts the fusion, spin, and braiding behavior of anyonic excitations after gauging. We demonstrate this for the electric-magnetic self-dual ZN{\mathbb{Z}}_{N}ZN​ gauge theory, the twofold symmetric SU(3)1\text{SU}{(3)}_{1}SU(3)1​, and the S3{S}_{3}S3​-symmetric SO(8)1\text{SO}{(8)}_{1}SO(8)1​ Wess-Zumino-Witten theories.