Holographic complexity of conformal fields in global de Sitter spacetime

TL;DR

This paper calculates the holographic complexity of conformal fields in global de Sitter spacetime using volume and action methods, comparing results across different holographic setups.

Contribution

It introduces a novel computation of holographic complexity for conformal fields in global de Sitter spacetime via two distinct holographic approaches.

Findings

Complexity computed for CFT on global dS boundary using volume and action prescriptions.

Comparison of complexity results between boundary and brane setups in AdS spacetime.

Analysis of differences with previous holographic complexity results in de Sitter patches.

Abstract

We compute the holographic complexity of conformal quantum fields in rigid global de Sitter spacetime (dS$_{d}$) using the volume and action prescriptions. First we consider AdS$_{d+1}$ spacetime in global dS$_{d}$ foliations, and compute the complexity of the CFT supported on the global dS$_{d}$ conformal boundary. Next, we consider CFT supported on a global dS$_d$ (UV) brane embedded in AdS$_{d+1}$ spacetime, and compute the holographic complexity in this brane set up. We compare and contrast the results in the two cases, as well as with related results in the literature obtained in alternative holographic set ups involving patches of de Sitter spacetime covered by static coordinates or conformal (Poincar\'e) coordinates.