Narain CFTs from quantum codes and their ${\mathbb{Z}}_2$ gauging

We investigate the gauging of a ${\mathbb{Z}}_2$ symmetry in Narain conformal field theories (CFTs) constructed from qudit stabilizer codes. Considering both orbifold and fermionization, we establish a connection between ${\mathbb{Z}}_2$ gauging procedures and modifications of the momentum lattice by vectors characterizing the ${\mathbb{Z}}_2$ symmetry. We also provide three-dimensional interpretations of ${\mathbb{Z}}_2$ gaugings through abelian Chern-Simons theories, which act as symmetry topological field theories.