Speaker
Description
We revisit the reconstruction of a free scalar in 4-dimensional Lorentzian Anti-de-Sitter spacetime in terms of primary operators in the boundary 3d CFT. We show that the positive and negative energy subspaces of solutions to the Klein–Gordon equation in AdS can be spanned with bulk-to-boundary propagators with appropriate time orderings. As a result, free scalar fields on a codimension-1 bulk hypersurface can be expressed in terms of operators integrated over boundary regions in the past or future of the hypersurface with kernels given by time-ordered or anti-time-ordered propagators. We will explain how to obtain a similar decomposition of the free field in terms of boundary operators transforming in representations of an so(3,1) subalgebra of the 4d AdS isometry algebra by constructing the appropriate wavefunctions. We conclude by showing that the expansion of a free scalar in Minkowski space in plane wave, Carrollian and conformal primary bases follow from these results in various flat space limits.