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Gravitational Wilson lines in 3D de Sitter. (English) Zbl 1451.83057

Summary: We construct local probes in the static patch of Euclidean \(\mathrm{dS}_3\) gravity. These probes are Wilson line operators, designed by exploiting the Chern-Simons formulation of 3D gravity. Our prescription uses non-unitary representations of \(so(4) \simeq su(2)_L \times su(2)_R\), and we evaluate the Wilson line for states satisfying a singlet condition. We discuss how to reproduce the Green’s functions of massive scalar fields in \(\mathrm{dS}_3\), the construction of bulk fields, and the quasinormal mode spectrum. We also discuss the interpretation of our construction in Lorentzian signature in the inflationary patch, via \(\mathrm{SL}(2, \mathbb{C})\) Chern-Simons theory.

MSC:

83C80 Analogues of general relativity in lower dimensions
58J28 Eta-invariants, Chern-Simons invariants
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