We construct a unitary, modular-invariant torus partition function of a two-dimensional conformal field theory with a Virasoro primary spectral gap of ${\mathrm{\Delta }}_{*}=[(c-1)/12]$ above the vacuum. The twist gap is identical, apart from two states ${\mathcal{O}}_{*}$ with spin scaling linearly in the central charge $c$. These states admit an ${\mathrm{AdS}}_3$ interpretation as strongly coupled strings. All other states are black hole microstates.

• Received 14 September 2023
• Accepted 21 December 2023

DOI:https://doi.org/10.1103/PhysRevLett.132.041602

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Published by the American Physical Society