Supersymmetry and Sum Rules in the Goldberger-Wise Model

TL;DR

This paper reveals a hidden supersymmetric structure in the Goldberger-Wise model's gravitational and scalar sectors, which helps derive sum rules ensuring controlled high-energy behavior of massive spin-2 states.

Contribution

It uncovers a dual N=2 supersymmetry in the GW model, generalizing previous findings and linking mode properties to establish sum rules for scattering amplitudes.

Findings

Identifies a hidden supersymmetry in the GW model.

Derives sum rules for spin-2 scattering amplitudes.

Explains the form of spin-0 mode equations and boundary conditions.

Abstract

In this work we demonstrate that the mixed gravitational and scalar sectors of the five-dimensional Goldberger-Wise (GW) model, in which the size of a warped extra dimension is dynamically determined, has a "hidden" dual $N=2$ supersymmetric structure. This symmetry structure, a generalization of one found in the unstabilized Randall-Sundrum model, is a result of the spontaneously broken five-dimensional diffeomorphism invariance of the underlying gravitational theory. The supersymmetries relate the properties of the spin-1 and spin-0 modes "eaten" by the massive spin-2 Kaluza-Klein states of the theory to the mode functions of the spin-2 modes. Because the symmetries relate the couplings and masses of the massive spin-2 states to those of the tower of physical spin-0 states of the GW model, they enable us to analytically prove the sum rule relations which ensure the tree-level scattering amplitudes of the massive spin-2 states will grow no faster than ${\cal O}(s)$. The analysis given here also explains the unconventional forms of the spin-0 mode equation, boundary condition(s), and normalization found in the GW model.