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A universal inequality on the unitary 2D CFT partition function

A universal inequality on the unitary 2D CFT partition function

We prove the conjecture proposed by Hartman, Keller and Stoica [HKS14]: the grand-canonical free energy of a unitary 2D CFT with a sparse spectrum below the scaling dimension $\frac{c}{12}+\epsilon$ and below the twist $\frac{c}{12}$ is universal in the large $c$ limit for all $\beta_L\beta_R \neq 4\pi^2$. The technique of the …