Dimensionally reducing the classical Regge growth conjecture

TL;DR

This paper investigates how the classical Regge growth conjecture constrains the spectrum of 4d effective theories derived from higher-dimensional Einstein gravity compactifications, revealing specific conditions on massive spin-2 modes.

Contribution

It demonstrates that the conjecture imposes non-trivial constraints on the 4d spectrum, particularly on the number and mass ratios of massive spin-2 modes, which are not apparent in the higher-dimensional theory.

Findings

The 4d spectrum must have either no or infinitely many massive spin-2 modes.

Mass ratios between consecutive Kaluza-Klein spin-2 modes are bounded by 4d coupling constants.

Higher-dimensional Einstein gravity automatically satisfies the conjecture, but it constrains the 4d effective theory.

Abstract

We explore the classical Regge growth conjecture in the 4d effective field theory that results from compactifying $D$-dimensional General Relativity on a compact, Ricci-flat manifold. While the higher dimensional description is given in terms of pure Einstein gravity and the conjecture is automatically satisfied, it imposes several non-trivial constraints in the 4d spectrum. Namely, there must be either none or an infinite number of massive spin-2 modes, and the mass ratio between consecutive Kaluza-Klain spin-2 replicas is bounded by the 4d coupling constants.