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Hidden Conformal Symmetry of the Discrete Series Scalars in dS$_2$

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arxiv 2410.19041 v1 pith:JH3CJQXQ submitted 2024-10-24 hep-th gr-qc

Kara Farnsworth , Kurt Hinterbichler , Samanta Saha This is my paper · ORCID
classification hep-thgr-qc
keywords conformalinvariantshiftsymmetryfieldsconformallydiscretedual
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

In $D$ dimensional de Sitter space, a scalar field has an infinite tower of special tachyonic mass values at which enhanced shift symmetries appear. After modding out by these shift symmetries, these fields correspond to the unitary irreducible representations of the de Sitter group known as the discrete series. We show that in $D=2$ these theories have global conformal symmetry. In all but the massless case, these theories have no stress tensor and the conformal symmetry does not act in the usual way on the scalar field. We find the conformal symmetry by explicitly computing the correlators of the shift invariant local operators and showing that they take conformally invariant forms. We also demonstrate how these fields are self dual in $D=2$, and dual to the shift invariant massive vector fields, which are therefore also conformally invariant.

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Cited by 3 Pith papers

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

  1. 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.

  2. Revealing the conformal symmetry of the discrete series scalars in dS${}_2$

    hep-th 2026-07 conditional novelty 6.0 of 10

    Massive discrete-series scalars in dS2 admit an on-shell global conformal symmetry realized non-locally on the scalar and locally on a conformal Killing tensor, with a traceless stress tensor generating SL(2,R)×SL(2,R).

  3. Higher-order chiral scalar from boundary reduction of 3d higher-spin gravity

    hep-th 2025-01 conditional novelty 6.0 of 10

    Boundary reduction of 3d higher-spin Chern-Simons gravity yields covariant and gauge-fixed higher-derivative chiral-scalar actions for arbitrary spin s, with a factorized kinetic operator and special zero-mode backgrounds.

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