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Even the photon propagator must break de Sitter symmetry
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The propagator for the massless vector field in de Sitter space cannot maintain de Sitter invariance in the general covaraint gauge, except in the exactly transverse gauge limit. This is due to a previously overlooked Ward-Takahashi identity that the propagator must satisfy. Here we construct the propagator that satisfies all the conditions of a consistently quantized theory. Our solution preserves cosmological symmetries and dilations, but breaks spatial special conformal transformations. The solution amounts to adding a homogeneous de Sitter breaking term to previously reported de Sitter invariant solutions of the propagator equation of motion. Even though the corrections we report pertain to the gauge sector of the linear theory, they are relevant and have to be accounted for when interactions are included.
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Cited by 3 Pith papers
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A remarkably simple covariant graviton propagator in Anti-de Sitter spacetime
A special gauge choice (β=1, α=4(d+2)/d) yields a simple graviton propagator in (A)dS satisfying ∇^μ μ ∇^ν μ G_{μν,α'β'} = 0.
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De Sitter quantum gravity within the covariant Lorentzian approach to asymptotic safety
In the Einstein-Hilbert truncation on de Sitter, the Lorentzian FRG flow exhibits a non-Gaussian UV fixed point for ζ=1/2 and ζ=1 gauges over restricted parameter ranges.
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Bulk-to-bulk photon propagator in AdS
The bulk-to-bulk photon propagator in Euclidean AdS is derived in axial, Coulomb and covariant gauges, with the simplest position-space form in the Fried–Yennie gauge ξ=d/(d−2).
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