Reviving QFT in ( 2 + 1 )-dimensional de Sitter spacetime

D’Amico, Guido; Kaloper, Nemanja

doi:10.1103/PhysRevD.110.125022

Reviving QFT in ( $2 + 1$ )-dimensional de Sitter spacetime

Journal Article · Mon Dec 23 00:00:00 EST 2024 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.110.125022· OSTI ID:2483640

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We consider a conformally coupled scalar quantum field theory (QFT) on ( $2 + 1$ )-dimensional static Einstein universe $R \times S^{2}$ and write down the free theory Hilbert space. We explain that this theory is secretly a QFT in ( $2 + 1$ )-dimensional de Sitter space because all the quantum observables experience “quantum revivals,” which naturally restricts the timelike $R$ to the appropriate de Sitter time range. Our construction circumvents the causal obstruction to formulating QFT in de Sitter due to event horizons. There are not any in static Einstein. The “unitary gauge” description of the theory is realized by the zonal harmonics $P_{ℓ} (\hat{n} \cdot {\hat{n}}^{'})$ . We verify that interactions with conformally invariant external sources are mediated only by these modes. Hence these modes comprise the complete basis of the “bulk” theory. When the theory is cut off in the UV, the basis dimension scales as the Bekenstein-Hawking formula.

Published by the American Physical Society 2024

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009999

OSTI ID:: 2483640

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 12 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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