标题： 宇宙学CPT定理 显示英文标题

标题： The Cosmological CPT Theorem

摘要： CPT定理指出，一个幺正且洛伦兹不变的理论也必须对一种离散对称性 $\mathbf{CRT}$ 不变，该对称性反转电荷、时间以及一个空间方向。 本文研究了一个 $\mathbb{Z}_2 \times \mathbb{Z}_2$ 对称性群，在其中两个非平凡对称性（“反射现实”和180度旋转）分别由幺正性和洛伦兹不变性推导而来，而第三个对称性是 $\mathbf{CRT}$。（在宇宙学中，尺度不变性扮演着洛伦兹不变性的角色。） 这自然引出了CPT定理的逆命题，因为任意两个离散的 $\mathbb{Z}_2$ 对称性都会推出第三个。 此外，在许多场论中，“反射现实” $\mathbb{Z}_2$ 对称性实际上足以表明理论在耦合范围的一般情况下是完全幺正的。 基于之前关于宇宙光学定理的研究，我们在任意维度上推导了与整体反射现实（在所有平坦的FLRW模型中）和 $\mathbf{CRT}$ （在de Sitter时空）相关的非微扰现实条件。 令人惊讶的是，这个 $\mathbf{CRT}$ 约束足以确定波函数系数在未来无穷远处的相位（除了一个实数符号外）——无需任何解析延拓，也不需要与过去无穷远进行比较——尽管在整体理论具有对数UV或IR发散的情况下需要额外注意。 这一结果对de Sitter全息论具有重要意义，因为它使我们能够确定对偶CFT中任意$n$-点函数的相位。 显示英文摘要

摘要： The CPT theorem states that a unitary and Lorentz-invariant theory must also be invariant under a discrete symmetry $\mathbf{CRT}$ which reverses charge, time, and one spatial direction. In this article, we study a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry group, in which two of the nontrivial symmetries (``Reflection Reality'' and a 180 degree rotation) are implied by Unitarity and Lorentz Invariance respectively, while the third is $\mathbf{CRT}$. (In cosmology, Scale Invariance plays the role of Lorentz Invariance.) This naturally leads to converses of the CPT theorem, as any two of the discrete $\mathbb{Z}_2$ symmetries will imply the third one. Furthermore, in many field theories, the Reflection Reality $\mathbb{Z}_2$ symmetry is actually sufficient to imply the theory is fully unitary, over a generic range of couplings. Building upon previous work on the Cosmological Optical Theorem, we derive non-perturbative reality conditions associated with bulk Reflection Reality (in all flat FLRW models) and $\mathbf{CRT}$ (in de Sitter spacetime), in arbitrary dimensions. Remarkably, this $\mathbf{CRT}$ constraint suffices to fix the phase of all wavefunction coefficients at future infinity (up to a real sign) -- without requiring any analytic continuation, or comparison to past infinity -- although extra care is required in cases where the bulk theory has logarithmic UV or IR divergences. This result has significant implications for de Sitter holography, as it allows us to determine the phases of arbitrary $n$-point functions in the dual CFT.