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

TL;DR

This paper explores how gauging a $Z_2$ symmetry in Narain CFTs derived from quantum codes affects their structure, linking lattice modifications to topological field theories and broadening understanding of symmetry gauging in these models.

Contribution

It establishes a connection between $Z_2$ gauging procedures and lattice modifications in Narain CFTs from quantum codes, including orbifold, fermionization, and topological interpretations.

Findings

$Z_2$ gauging modifies momentum lattices via specific vectors.

Connections between gauging procedures and lattice modifications are established.

Three-dimensional Chern-Simons theories provide topological interpretations of $Z_2$ gaugings.

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.