The World-Line Quantum Mechanics Model at Finite Temperature which is Dual to the Static Patch Observer in de Sitter Space

TL;DR

This paper introduces a conformal quantum mechanics model that accurately reproduces the Green functions and conformal weights of scalar fields in de Sitter space, connecting it to finite-temperature Schwinger-Keldysh formalism.

Contribution

It proposes a new simple quantum mechanics model that captures the behavior of scalar fields in de Sitter space and extends to a large-N matrix model in Schwarzschild de Sitter space.

Findings

Model reproduces retarded Green functions and conformal weights.

Action integral expressed via complex contour integral, indicating finite temperature.

Extension to large-N matrix model in Schwarzschild de Sitter space.

Abstract

A simple conformal quantum mechanics model of a d-component variable is proposed, which exactly reproduces the retarded Green functions and conformal weights of conformally coupled scalar fields in de Sitter spacetime seen by a static patch observer. It is found that the action integral of this model is automatically expressed by a complex integral over the time variable t along a closed contour in a way which is typical to the Schwinger-Keldysh formalism of a thermofield theory. Hence this model is at finite temperature. The case of conformally coupled scalar fields in 3d Schwarzschild de Sitter space is also considered and then a large-N matrix model is obtained.