12:30 pm 3rd Floor Atrium
Wilson Spools and de Sitter Quantum Gravity.
I will propose a mechanism, based on the Chern-Simons formulation of three-dimensional Euclidean gravity, that couples matter fields to three-dimensional de Sitter quantum gravity. First, I will derive su(2) representations that differ in Hermiticity choice from the usual unitary representations; these are important for gravitational applications of Chern-Simons theory. I will then introduce the concept of a “Wilson spool” constructed from a collection of Wilson loops winding around Euclidean de Sitter space. In the classical limit, this spool correctly reproduces the one-loop determinant of a free massive scalar field on the three-sphere. Allowing for quantum metric fluctuations, it can be systematically evaluated to any order in perturbation theory. I will finish with some work in progress using the spool to extend the Selberg zeta function, a method for computing one-loop determinants for hyperbolic quotients, to more general spacetimes.