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  • Letter
  • Open Access

From AdS to dS exchanges: Spectral representation, Mellin amplitudes, and crossing

Charlotte Sleight*

Massimo Taronna†

  • School of Natural Sciences, Institute for Advanced Study, 1 Einstein Drive, Princeton, New Jersey 08540, USA and Université Libre de Bruxelles and International Solvay Institutes, Brussels CP231, Belgium

  • Dipartimento di Fisica “Ettore Pancini”, Università degli Studi di Napoli Federico II, Monte S. Angelo, Via Cintia, 80126 Napoli, Italy, INFN, Sezione di Napoli, Monte S. Angelo, Via Cintia, 80126 Napoli, Italy, Department of Physics, Princeton University, Jadwin Hall, Princeton, New Jersey 08544, USA and Scuola Superiore Meridionale, Università degli Studi di Napoli Federico II, Largo San Marcellino 10, 80138 Napoli, Italy

  • *csleight@ias.edu
  • †massimo.taronna@unina.it
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Phys. Rev. D 104, L081902 – Published 21 October, 2021

DOI: https://doi.org/10.1103/PhysRevD.104.L081902

Abstract

In this paper we take the first steps towards bridging the gap between the conformal and cosmological bootstrap programs. We present a simple general relation between tree-level exchanges in anti-de Sitter (AdS) and de Sitter (dS) space with Bunch-Davies intial conditions, providing a complete AdS to dS dictionary at tree-level. This allows us to directly import techniques and results for conformal field theory correlators dual to AdS-Witten diagrams to boundary correlation functions in dS. We apply this relation to extend various indispensable tools from the conformal bootstrap to boundary correlation functions in dS, including Mellin amplitudes and the spectral representation for dS exchanges. We also derive their conformal block decomposition, both in the direct and crossed channels, from their AdS counterparts. The relation between AdS and dS exchanges itself is derived using a recently introduced Mellin-Barnes representation for boundary correlators in momentum space, where (A)dS exchanges are straightforwardly fixed by a combination of factorization, conformal symmetry and boundary conditions.

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Phys. Rev. D 104, L081902– Published 21 October, 2021
  • Received 19 August 2020
  • Accepted 29 September 2021
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