A Transfer Matrix Method for Resonances in Randall-Sundrum Models III: An analytical comparison

TL;DR

This paper compares numerical and analytical transfer matrix methods for analyzing resonances in Randall-Sundrum models, providing new exact solutions for various fields and confirming the methods' agreement.

Contribution

It introduces new exact solutions for multiple fields in Randall-Sundrum models and validates the transfer matrix method through detailed comparison with analytical results.

Findings

Perfect agreement between numerical and analytical resonance calculations.

New exact solutions for scalar, gauge, Kalb-Ramond, and q-form fields.

Validation of the transfer matrix method in models with and without dilaton coupling.

Abstract

The transfer matrix method is used to analyze resonances in Randall-Sundrum models. Although it has successfully been used previously by us we provide here a comparison between the numerical and analytical models. To reach this we first find new exact solution for the scalar, gauge, Kalb-Ramond and $q-$form fields. Them we calculate numerically the resonances by the transfer matrix method and compare with the analytical result. For completeness, this is done for models with and without the dilaton coupling. The results show a perfect agreement between the analytical and numerical methods.