QFT, String Temperature and the String Phase of De Sitter Space-time

TL;DR

This paper explores the relationship between quantum field theory and string theory in de Sitter space, introducing a dual transform linking classical and quantum string lengths, and analyzing the back reaction effects leading to two curvature phases.

Contribution

It introduces a dual transform connecting QFT and string theory in de Sitter space and analyzes the back reaction, revealing two distinct curvature phases sustained by strings.

Findings

The string temperature in de Sitter space is the dual of the QFT-Hawking-Gibbons temperature.

De Sitter space admits two curvature solutions: classical low curvature and quantum high curvature.

A maximal curvature value exists due to string back reaction, supporting a stringy phase.

Abstract

The density of mass levels \rho(m) and the critical temperature for strings in de Sitter space-time are found. QFT and string theory in de Sitter space are compared. A `Dual'-transform is introduced which relates classical to quantum string lengths, and more generally, QFT and string domains. Interestingly, the string temperature in De Sitter space turns out to be the Dual transform of the QFT-Hawking-Gibbons temperature. The back reaction problem for strings in de Sitter space is addressed selfconsistently in the framework of the `string analogue' model (or thermodynamical approach), which is well suited to combine QFT and string study.We find de Sitter space-time is a self-consistent solution of the semiclassical Einstein equations in this framework. Two branches for the scalar curvature R(\pm) show up: a classical, low curvature solution (-), and a quantum high curvature solution (+), enterely sustained by the strings. There is a maximal value for the curvature R_{\max} due to the string back reaction. Interestingly, our Dual relation manifests itself in the back reaction solutions: the (-) branch is a classical phase for the geometry with intrinsic temperature given by the QFT-Hawking-Gibbons temperature.The (+) is a stringy phase for the geometry with temperature given by the intrinsic string de Sitter temperature. 2 + 1 dimensions are considered, but conclusions hold generically in D dimensions.