Quantum subsystem codes, CFTs and their ${\mathbb{Z}}_2$-gaugings

Abstract

We construct Narain conformal field theories (CFTs) from quantum subsystem codes, a more comprehensive class of quantum error-correcting codes than quantum stabilizer codes, for qudit systems of prime dimensions. The resulting code CFTs exhibit a global ${\mathbb{Z}}_2$ symmetry, enabling us to perform the ${\mathbb{Z}}_2$-gauging to derive their orbifolded and fermionized theories when the symmetry is non-anomalous. We classify a subset of these subsystem code CFTs using weighted oriented graphs and enumerate those with small central charges. Consequently, we identify several bosonic code CFTs self-dual under the ${\mathbb{Z}}_2$-orbifold, new supersymmetric code CFTs, and a few fermionic code CFTs with spontaneously broken supersymmetry.

47 pages, 1 figure; v2: typos corrected, minor changes, published version