Casimir Energy of AdS5 Electromagnetism and Cosmological Constant Problem

TL;DR

This paper calculates the Casimir energy in 5D warped geometry, introduces a new regularization method based on minimal area principles, and explores its implications for the cosmological constant problem.

Contribution

It presents a novel sphere lattice regularization method for Casimir energy in warped geometries and analyzes its dependence on model parameters.

Findings

Casimir energy expressed in a closed form.

Warp parameter exhibits renormalization effects.

New interpretation of Casimir energy with quantized 4D momenta.

Abstract

Casimir energy is calculated for the 5D electromagnetism in the warped geometry. It is compared with the flat case(arXiv:0801.3064). A new regularization, called sphere lattice regularization, is taken. It is based on the minimal area principle and is a direct realization of the geometrical approach to the renormalization group. The properly regularized form of Casimir energy, is expressed in a closed form. We numerically evaluate $\La$(4D UV-cutoff), $\om$(5D bulk curvature, warp parameter) and $T$(extra space IR parameter) dependence of the Casimir energy. The warp parameter $\om$ suffers from the renormalization effect. We examine the meaning of the weight function and finally reach a new definition of the Casimir energy where the 4D momenta(or coordinates) are quantized with the extra coordinate as the Euclidean time. We comment on the cosmological term at the end.