Operator origin of anomalous dimensions in de Sitter space

Journal Article · 11 May 2025 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.111.103513 · OSTI ID:2565759

Cohen, Timothy; Green, Daniel; Huang, Yiwen

The late-time limit of the power spectrum for heavy (principal series) fields in de Sitter (dS) 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 space. 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 nondynamical “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. Published by the American Physical Society 2025

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0009919; SC0011640
• OSTI ID: 2565759
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 10 Vol. 111; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English