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Résumé |
There is a deep relation between classical error-correcting
codes, Euclidean lattices, and chiral 2d CFTs. We show this relation
extends to include quantum codes, Lorentzian lattices, and non-chiral
CFTs. The relation to quantum codes provides a simple way to solve
modular bootstrap constraints and identify interesting examples of
conformal theories. In particular we construct many examples of
physically distinct isospectral theories, examples of "would-be" CFT
partition function -- non-holomorphic functions satisfying all
constraints of the modular bootstrap, yet not associated with any
known CFT, and find theory with the maximal spectral gap among all
Narain CFTs with the central charge c=4. We also discuss averaging
over the ensemble of all CFTs associated with quantum codes, and its
possible holographic interpretation. The talk is based on
arXiv:2009.01236 and arXiv:2009.01244. |
