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德西特空间中反常维度的算符起源

Operator Origin of Anomalous Dimensions in de Sitter Space

Timothy Cohen, Daniel Green, Yiwen Huang

AI总结:

本文针对德西特空间中算符标度行为微扰修正与量子场幺正演化看似矛盾的问题,利用Mellin空间计算两点函数中标度维度的单圈修正,并通过在SdSET中引入非动力学算符实现UV与有效理论的匹配,验证了其与幺正性、正定性的一致性。

摘要:

德西特空间中重(主系列)场的功率谱的晚期极限会产生一系列带有复标度维度的多项式项。这类标度行为被认为源自一个具有复维度的关联算符。在自由理论中,已知这些复维度满足幺正性对态空间施加的约束。然而,算符标度行为的微扰修正乍看之下与德西特空间中量子场的幺正演化并不一致。本文展示了如何从基于局域算符的场论描述出发,计算两点函数中出现的标度维度的单圈修正。我们首先说明如何利用Mellin空间计算这些反常维度,该空间的特点是可自然适配无标度调节器。随后我们探究了长波极限下出现的Soft de Sitter Effective Theory(软德西特有效理论,SdSET)描述所带来的影响。要在紫外描述与SdSET描述之间实现精细匹配,需要在有效理论中引入新型的非动力学“算符”。这不仅是重现从Källén-Lehmann谱表示(直接利用幺正态空间得到)中提取的结果的必要条件,也得到了调用正定性的一般性论证的支持。

英文摘要:

The late time limit of the power spectrum for heavy (principal series) fields in de Sitter space yields a series of polynomial terms with complex scaling dimensions. Such scaling behavior is expected to result from an associated operator with a complex dimension. In a free theory, these complex dimensions are known to match the constraints imposed by unitarity on the space of states. Yet, perturbative corrections to the scaling behavior of operators are naively inconsistent with unitary evolution of the quantum fields in dS. This paper demonstrates how to compute one-loop corrections to the scaling dimensions that appear in the two point function from the field theory description in terms of local operators. We first show how to evaluate these anomalous dimensions using Mellin space, which has the feature that it naturally accommodates a scaleless regulator. We then explore the consequences for the Soft de Sitter Effective Theory (SdSET) description that emerges in the long wavelength limit. Carefully matching between the UV and SdSET descriptions requires the introduction of novel non-dynamical "operators" in the effective theory. This is not only necessary to reproduce results extracted from the Källén-Lehmann representation (that use the space of unitary states directly), but it is also required by general arguments that invoke positivity.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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