Casimir Energy in Deconstruction and the Cosmological Constant

TL;DR

This paper shows how to compute finite Casimir energies in deconstructed models, enabling a well-defined way to estimate vacuum energy contributions that could explain the small positive cosmological constant observed.

Contribution

It introduces a method to transfer Casimir energy calculations from higher-dimensional theories to four-dimensional deconstructed models, providing a new approach to address the cosmological constant problem.

Findings

Large kink masses suppress Casimir energy exponentially.

The model yields a small, positive vacuum energy consistent with observations.

A well-defined prescription for finite vacuum energy in deconstructed theories.

Abstract

We demonstrate that by employing the correspondence between gauge theories in geometric and in deconstructed extra dimensions, it is possible to transfer the methods for calculating finite Casimir energy densities in higher dimensions to the four-dimensional deconstruction setup. By this means, one obtains an unambiguous and well-defined prescription to determine finite vacuum energy contributions of four-dimensional quantum fields which have a higher-dimensional correspondence. Thereby, large kink masses lead to an exponentially suppressed Casimir effect. For a specific model we hence arrive at a small and positive contribution to the cosmological constant in agreement with observations.