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Hilbert space of Quantum Field Theory in de Sitter spacetime

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arxiv 2301.04146 v2 pith:EH2A5VCU submitted 2023-01-10 hep-th gr-qc

Joao Penedones , Kamran Salehi Vaziri , Zimo Sun This is my paper
classification hep-thgr-qc
keywords fieldtheoryquantumsitterspacetimeconformalgrouphilbert
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We study the decomposition of the Hilbert space of quantum field theory in $(d+1)$ dimensional de Sitter spacetime into Unitary Irreducible Representations (UIRs) of its isometry group \SO$(1,d+1)$. Firstly, we consider multi-particle states in free theories starting from the tensor product of single-particle UIRs. Secondly, we study conformal multiplets of a bulk Conformal Field Theory with symmetry group \SO$(2,d+1)$. Our main tools are the Harish-Chandra characters and the numerical diagonalization of the (truncated) quadratic Casimir of \SO$(1,d+1)$. We introduce a continuous density that encodes the spectrum of irreducible representations contained in a reducible one of $\SO(1,d+1)$. Our results are complete for $d=1$ and $d=2$. In higher dimensions, we rederive and extend several results previously known in the literature. Our work provides the foundation for future nonperturbative bootstrap studies of Quantum Field Theory in de Sitter spacetime.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Ising the way into de Sitter

    hep-th 2026-07 conditional novelty 8.0 of 10

    The two-dimensional thermal Ising model on de Sitter provides exact cosmological correlators that stay finite at late times, with perturbative secular logarithms resummed into principal-series oscillations.

  2. Propagator positivity bounds for cosmological correlators

    hep-th 2025-12 conditional novelty 7.0 of 10

    An infinite tower of two-sided positivity bounds constrains the EFT coefficients of heavy fields on de Sitter, ruling out correlators with no unitary/causal UV completion.

  3. A discrete series gauge field at the late-time boundary of $dS_4$

    hep-th 2026-07 accept novelty 6.0 of 10

    Both Δ=1 and Δ=2 late-time Maxwell operators on planar dS4 furnish the photon unitary discrete series of SO(4,1), which splits into opposite-helicity summands via self-dual field-strength sectors.

  4. Microstate counting from defects in de Sitter

    hep-th 2025-11 conditional novelty 6.0 of 10

    Counting defect microstates via Lorentzian wormholes reproduces the de Sitter and Schwarzschild-de Sitter entropy area laws.

  5. Cosmological correlators in gravitationally-constrained de Sitter states

    hep-th 2025-07 conditional novelty 6.0 of 10

    Cosmological correlators in gravitationally constrained de Sitter states are conformally invariant and differ from QFT vacuum correlators, but relational observables with a heavy background state can reproduce QFT results.

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