Mass Hierarchies and Dynamical Field Range

TL;DR

This paper investigates how mass hierarchies influence the effective field range in quantum gravity, revealing that multi-field dynamics can extend the validity of EFT beyond naive geodesic approximations.

Contribution

It demonstrates that the dynamical field range differs from the geodesic distance when no mass hierarchy exists, and shows how a hierarchy can extend the EFT's validity in string compactifications.

Findings

Trajectory of light fields often deviates from geodesics without mass hierarchy.

Heavy field stabilization may not capture light field dynamics accurately.

Mass hierarchy can delay EFT breakdown, extending its effective range.

Abstract

Several swampland conjectures suggest that there is a critical field range beyond which the effective field theory (EFT) description breaks down in quantum gravity. In applications of these conjectures, however, the field range of interest is the field space distance traced by the physical trajectory that solves the equations of motion. We refer to this field space distance as the dynamical field range. We show that in the absence of a mass hierarchy between the light and heavy fields, the trajectory of the light field does not, in general, follow a geodesic in field space. Then, stabilizing the heavy fields at the minimum of their potential does not accurately describe the dynamics of the light field in general. A mass hierarchy can delay the breakdown of the EFT, and extend the effective field range. We illustrate these subtleties of multi-field dynamics with axions in Type II string compactifications.