Reconstruction of field theory from excitation spectra of defects

TL;DR

This paper presents a method to reconstruct underlying field theories from the excitation spectra of topological defects, successfully applied to known models and potentially useful for cosmological inflation analysis.

Contribution

It introduces a novel recipe for reconstructing field theories from defect spectra, applicable to both particle physics models and cosmological scenarios.

Findings

Successfully reconstructs sine-Gordon and λϕ^4 theories from spectra

Provides a method to infer inflaton potentials from defect spectra

Suggests defects as evidence for inflationary models

Abstract

We show how to reconstruct a field theory from the spectrum of bound states on a topological defect. We apply our recipe to the case of kinks in 1+1 dimensions with one or two bound states. Our recipe successfully yields the sine-Gordon and $\lambda \phi^4$ field theories when suitable bound state spectra are assumed. The recipe can also be used to globally reconstruct the inflaton potential of inflationary cosmology if the inflaton produces a topological defect. We discuss how defects can provide ``smoking gun'' evidence for a class of inflationary models.