On the renormalization group for the interacting massive scalar field theory in curved space

TL;DR

This paper derives the effective action for an interacting massive scalar field in curved spacetime using heat-kernel methods, analyzing the renormalization group flow of coupling constants from high to low energies.

Contribution

It introduces a smooth quadratic form for low-energy decoupling and investigates the evolution of coupling parameters in curved space.

Findings

Decoupling of scalar coupling constants at low energies

Flow of nonminimal interaction parameter from conformal value

Analysis within toy models with different coupling signs

Abstract

The effective action for the interacting massive scalar field in curved space-time is derived using the heat-kernel method. Starting from this effective action, we establish a smooth quadratic form of the low-energy decoupling for the four-scalar coupling constant and for the nonminimal interaction parameter. The evolution of this parameter from the conformal value 1/6 at high energies down to the IR regime is investigated within the two toy models with negative and positive four-scalar coupling constants.