We extend the holographic formulation of the semiclassical no-boundary wave
function (NBWF) to models with Maxwell vector fields. It is shown that the
familiar saddle points of the NBWF have a representation in which a regular,
Euclidean asymptotic AdS geometry smoothly joins onto a Lorentzian
asymptotically de Sitter universe through a complex transition region. The tree
level probabilities of Lorentzian histories are fully specified by the action
of the AdS region of the saddle points. The scalar and vector matter profiles
in this region are complex from an AdS viewpoint, with universal asymptotic
phases. The dual description of the semiclassical NBWF thus involves complex
deformations of Euclidean CFTs.Comment: 17 pages, 3 fig
