Bulk Renormalization and Particle Spectrum in Codimension-Two Brane Worlds

TL;DR

This paper calculates the Casimir energy in codimension-two brane worlds using advanced regularization techniques, exploring implications for supersymmetry, brane properties, and the cosmological constant in models with extra dimensions.

Contribution

It introduces a new method combining zeta function and dimensional regularization to sum over Kaluza-Klein states and analyzes how brane flux and supersymmetry affect the spectrum and vacuum energy.

Findings

Casimir energy depends on brane flux and geometry.

Partial supersymmetry survives with equal flux branes.

Implications for the cosmological constant in extra-dimensional models.

Abstract

We study the Casimir energy due to bulk loops of matter fields in codimension-two brane worlds and discuss how effective field theory methods allow us to use this result to renormalize the bulk and brane operators. In the calculation we explicitly sum over the Kaluza-Klein (KK) states with a new convenient method, which is based on a combined use of zeta function and dimensional regularization. Among the general class of models we consider we include a supersymmetric example, 6D gauged chiral supergravity. Although much of our discussion is more general, we treat in some detail a class of compactifications, where the extra dimensions parametrize a rugby ball shaped space with size stabilized by a bulk magnetic flux. The rugby ball geometry requires two branes, which can host the Standard Model fields and carry both tension and magnetic flux (of the bulk gauge field), the leading terms in a derivative expansion. The brane properties have an impact on the KK spectrum and therefore on the Casimir energy as well as on the renormalization of the brane operators. A very interesting feature is that when the two branes carry exactly the same amount of flux, one half of the bulk supersymmetries survives after the compactification, even if the brane tensions are large. We also discuss the implications of these calculations for the natural value of the cosmological constant when the bulk has two large extra dimensions and the bulk supersymmetry is partially preserved (or completely broken).