Gravitational Wilson Lines in 3D de Sitter

Abstract

We construct local probes in the static patch of Euclidean 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 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 $SL(2,\mathbb{C})$ Chern-Simons theory.

46 pages, 1 figure; v2: final version for JHEP, minor edits