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arXiv · 2609.16111

Classification of c=1 CFTs

Lorenz Eberhardt·Nat Levine
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Abstract

We completely classify unitary 2d CFTs with central charge $c=1$ and discrete spectrum. We confirm the folklore that the only such theories are the compact free boson, its $\mathbb{Z}_2$-orbifold, and three exceptional theories obtained as orbifolds of the SU(2)$_1$ WZW model. The proof is by recasting the $c=1$ modular bootstrap as a crystalline measure problem for the density of states, and analytically solving it. We also show that, once the density of states is specified, the full CFT can be uniquely reconstructed.

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Lorenz Eberhardt, Nat Levine. 2026-09-14. Classification of c=1 CFTs. https://arxiv.org/abs/2609.16111

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