Antipodally symmetric gauge fields and higher-spin gravity in de Sitter space

TL;DR

This paper investigates antipodally symmetric solutions for gauge fields of all spins in de Sitter space, revealing that boundary correlators vanish and discussing implications for higher-spin dS/CFT and initial value problems.

Contribution

It characterizes antipodally symmetric solutions for arbitrary spin fields in de Sitter space and explores their implications for higher-spin holography and boundary data.

Findings

Boundary 2-point functions vanish for free fields on dS_4/Z_2.

Higher-spin boundary n-point functions also vanish in Vasiliev theory.

The free-field results enable a well-posed initial value problem for interacting theories.

Abstract

We study gauge fields of arbitrary spin in de Sitter space. These include Yang-Mills fields and gravitons, as well as the higher-spin fields of Vasiliev theory. We focus on antipodally symmetric solutions to the field equations, i.e. ones that live on "elliptic" de Sitter space dS_4/Z_2. For free fields, we find spanning sets of such solutions, including boundary-to-bulk propagators. We find that free solutions on dS_4/Z_2 can only have one of the two types of boundary data at infinity, meaning that the boundary 2-point functions vanish. In Vasiliev theory, this property persists order by order in the interaction, i.e. the boundary n-point functions in dS_4/Z_2 all vanish. This implies that a higher-spin dS/CFT based on the Lorentzian dS_4/Z_2 action is empty. For more general interacting theories, such as ordinary gravity and Yang-Mills, we can use the free-field result to define a well-posed perturbative initial value problem in dS_4/Z_2.