Mass hierarchies and non-decoupling in multi-scalar field dynamics

TL;DR

This paper investigates how the curvature of field space influences scalar field perturbations, revealing non-decoupling effects that impact low-energy dynamics in multi-scalar theories relevant to inflation and string compactifications.

Contribution

It introduces a detailed analysis of non-decoupling effects caused by field space curvature on scalar perturbations, extending understanding of multi-field dynamics beyond simple decoupling assumptions.

Findings

Field space curvature causes mixing between light and heavy modes.

Trajectory turns induce significant effects on perturbations.

Non-decoupling influences low-energy effective theories.

Abstract

In this work we study the effects of field space curvature on scalar field perturbations around an arbitrary background field trajectory evolving in time. Non-trivial imprints of the 'heavy' directions on the low energy dynamics arise when the vacuum manifold of the potential does not coincide with the span of geodesics defined by the sigma model metric of the full theory. When the kinetic energy is small compared to the potential energy, the field traverses a curve close to the vacuum manifold of the potential. The curvature of the path followed by the fields can still have a profound influence on the perturbations as modes parallel to the trajectory mix with those normal to it if the trajectory turns sharply enough. We analyze the dynamical mixing between these non-decoupled degrees of freedom and deduce its non-trivial contribution to the low energy effective theory for the light modes. We also discuss the consequences of this mixing for various scenarios where multiple scalar fields play a vital role, such as inflation and low-energy compactifications of string theory.