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A radial variable for de Sitter two-point functions

by Manuel Loparco, Jiaxin Qiao, Zimo Sun

Submission summary

Authors (as registered SciPost users): Manuel Loparco
Submission information
Preprint Link: scipost_202405_00031v1  (pdf)
Date submitted: 2024-05-22 10:50
Submitted by: Loparco, Manuel
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
Approach: Theoretical

Abstract

We introduce a ``radial" two-point invariant for quantum field theory in de Sitter (dS) analogous to the radial coordinate used in conformal field theory. We show that the two-point function of a free massive scalar in the Bunch-Davies vacuum has an exponentially convergent series expansion in this variable with positive coefficients only. Assuming a convergent K\"allén-Lehmann decomposition, this result is then generalized to the two-point function of any scalar operator non-perturbatively. A corollary of this result is that, starting from two-point functions on the sphere, an analytic continuation to an extended complex domain is admissible. dS two-point configurations live inside or on the boundary of this domain, and all the paths traced by analytic continuation between dS and the sphere or between dS and Euclidean Anti-de Sitter are also contained within this domain.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
In refereeing

Reports on this Submission

Report #1 by Anonymous (Referee 1) on 2024-12-4 (Invited Report)

Strengths

1 - Develops a new coordinate system to represent the two-point correlators in dS.

2 - these new coordinates allow the correlators to be written in terms of a convergent expansion in the radial variable

3 - the convergence of the series makes proving analytic properties or positivity more straightforward.

4 - Although these results are only applied to the free-propagators, they can be used for any correlator via the Kallen-Lehmann representation

Weaknesses

1 - The demonstration of the utility of this new variable using a concrete example would have been helpful.

Report

The use of the Kallen-Lehmann representation and analytic continuation from the sphere to dS loop calculations has proven to be a powerful tool for understand loop corrections in de Sitter space. This paper introduces a new representation of the free Green's functions that are exponentially convergent, allowing one to prove a number of useful properties of the analytic properties of the two-point statistic in dS. The paper lacks physics examples where this new variable is useful, but given the existing literature with the many worked examples, many readers will know how to apply these techniques. I recommend publication in the current form.

Recommendation

Publish (surpasses expectations and criteria for this Journal; among top 10%)

  • validity: high
  • significance: high
  • originality: high
  • clarity: high
  • formatting: good
  • grammar: good

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