Vector Fields in Holographic Cosmology

TL;DR

This paper extends holographic models of the no-boundary wave function to include Maxwell vector fields, revealing how saddle points connect Euclidean AdS geometries to Lorentzian de Sitter universes and involve complex CFT deformations.

Contribution

It introduces a holographic formulation of the semiclassical no-boundary wave function with vector fields, showing the connection between Euclidean AdS and Lorentzian de Sitter geometries.

Findings

Saddle points have a Euclidean AdS to Lorentzian dS transition.

Probabilities are determined by the AdS action of saddle points.

Dual description involves complex deformations of Euclidean CFTs.

Abstract

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.