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

• URL: http://arxiv.org/abs/2405.18145v1
• Date: Tue, 28 May 2024 13:03:37 GMT
• Title: Quantum subsystem codes, CFTs and their $\mathbb{Z}_2$-gaugings
• Authors: Keiichi Ando, Kohki Kawabata, Tatsuma Nishioka,
• Abstract summary: We construct Narain conformal field theories from quantum subsystem codes. The resulting code CFTs exhibit a global $mathbbZ$ symmetry, enabling us to perform the orbifolded and fermionized theories. We identify several bosonic code CFTs self-dual under the $mathbbZ$-bifold, new supersymmetric code CFTs, and a few fermionic code CFTs with spontaneously broken supersymmetry.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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