Correlators of unitary quantum field theories in Lorentzian signature obey certain analyticity and positivity properties. For interacting unitary CFTs in more than two dimensions, we show that these properties impose general constraints on families of minimal twist operators that appear in the OPEs of primary operators. In particular, we rederive and extend the convexity theorem which states that for the family of minimal twist operators with even spins appearing in the reflection-symmetric OPE of any scalar primary, twist must be a monotonically increasing convex function of the spin. Our argument is completely non-perturbative and it also applies to the OPE of nonidentical scalar primaries in unitary CFTs, constraining the twist of spinning operators appearing in the OPE. Finally, we argue that the same methods also impose constraints on the Regge behavior of certain CFT correlators.

中文翻译：

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CFT 中的广义 Nachtmann 定理

洛伦兹签名中幺正量子场论的相关子服从一定的解析性和正性属性。对于二维以上的交互统一 CFT，我们表明这些属性对出现在主要算子的 OPE 中的最小扭曲算子族施加了一般约束。特别是，我们重新推导并扩展了凸性定理，该定理指出，对于出现在任何标量初级的反射对称 OPE 中的偶数自旋的最小扭曲算子族，扭曲必须是自旋的单调递增凸函数。我们的论点是完全非微扰的，它也适用于酉 CFT 中不同标量原色的 OPE，限制了出现在 OPE 中的纺纱算子的扭曲。最后，