On the Decoupling of Heavy Modes in Kaluza-Klein Theories

TL;DR

This paper investigates how heavy Kaluza-Klein modes influence the effective 4D theory, emphasizing their role in accurately predicting interactions among light modes, with a detailed example involving a 6D Einstein-Maxwell setup.

Contribution

It highlights the necessity of including heavy KK modes in effective theories to correctly capture observable interactions, providing a geometric interpretation in a specific model.

Findings

Heavy KK modes are essential for accurate interaction predictions.

Heavy modes can be interpreted as internal space deformations.

The study clarifies the decoupling behavior of heavy modes in KK theories.

Abstract

In this paper we examine the 4-dimensional effective theory for the light Kaluza-Klein (KK) modes. Our main interest is in the interaction terms. We point out that the contribution of the heavy KK modes is generally needed in order to reproduce the correct predictions for the observable quantities involving the light modes. As an example we study in some detail a 6-dimensional Einstein-Maxwell theory coupled to a charged scalar and fermions. In this case the contribution of the heavy KK modes are geometrically interpreted as the deformation of the internal space.