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Maximizing the spectral gap for free bosonic CFTs
We study the spectral gap $Δ_1$ of Narain CFTs, the smallest scaling dimension of a nonvacuum $U(1)^c_L\times U(1)^c_R$ primary, as a function on the Narain moduli space. Using the exceptional isomorphisms for $SO^+(2,2)$ and $SO^+(3,3)$, we prove the sharp bounds $Δ_1\le 2/3$ at $c=2$ and $Δ_1\le 3
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