Tachyons in de Sitter space and analytical continuation from dS/CFT to AdS/CFT

TL;DR

This paper explores the analytic continuation between de Sitter and anti-de Sitter spacetimes, revealing a connection between tachyon dynamics in de Sitter space and scalar particles in AdS, and extending dS/CFT to AdS/CFT duality.

Contribution

It demonstrates how AdS can be obtained from dS via analytic continuation, linking tachyon dynamics to scalar particles and extending the duality framework.

Findings

AdS can be derived from dS through analytic continuation.

Tachyon dynamics in dS relate to scalar particles in AdS.

dS/CFT duality extends to AdS/CFT via this continuation.

Abstract

We discuss analytic continuation from d-dimensional Lorentzian de Sitter (dS$_d$) to d-dimensional Lorentzian anti-de Sitter (AdS$_{d}$) spacetime. We show that AdS$_{d}$, with opposite signature of the metric, can be obtained as analytic continuation of a portion of dS$_d$. This implies that the dynamics of (positive square-mass) scalar particles in AdS$_{d}$ can be obtained from the dynamics of tachyons in dS$_d$. We discuss this correspondence both at the level of the solution of the field equations and of the Green functions. The AdS/CFT duality is obtained as analytic continuation of the dS/CFT duality.