Narain CFTs from quantum codes and their $${\mathbb{Z}}_{2}$$ gauging

Abstract

Abstract 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.