Deconstructing the Gel'fand--Yaglom method and vacuum energy from a theory space

TL;DR

This paper extends the discrete Gel'fand--Yaglom method to compute determinants of mass matrices in particle physics models like dimensional deconstruction and clockwork theory, enabling calculation of vacuum energies.

Contribution

It generalizes the Gel'fand--Yaglom method for mass matrices in complex theories, facilitating vacuum energy computations in new physics models.

Findings

Derived explicit formulas for determinants of mass matrices.

Provided vacuum energy expressions for deconstruction and clockwork models.

Enhanced computational tools for analyzing particle physics theories.

Abstract

The discrete Gel'fand--Yaglom theorem was studied several years ago. In the present paper, we generalize the discrete Gel'fand--Yaglom method to obtain the determinants of mass matrices which appear current works in particle physics, such as dimensional deconstruction and clockwork theory. Using the results, we show the expressions for vacuum energies in such various models.