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We study the Casimir energy due to bulk loops of matter fields incodimension-two brane worlds and discuss how effective field theory methodsallow us to use this result to renormalize the bulk and brane operators. In thecalculation we explicitly sum over the Kaluza-Klein (KK) states with a newconvenient method, which is based on a combined use of zeta function anddimensional regularization. Among the general class of models we consider weinclude a supersymmetric example, 6D gauged chiral supergravity. Although muchof our discussion is more general, we treat in some detail a class ofcompactifications, where the extra dimensions parametrize a rugby ball shapedspace with size stabilized by a bulk magnetic flux. The rugby ball geometryrequires two branes, which can host the Standard Model fields and carry bothtension and magnetic flux (of the bulk gauge field), the leading terms in aderivative expansion. The brane properties have an impact on the KK spectrumand therefore on the Casimir energy as well as on the renormalization of thebrane operators. A very interesting feature is that when the two branes carryexactly the same amount of flux, one half of the bulk supersymmetries survivesafter the compactification, even if the brane tensions are large. We alsodiscuss the implications of these calculations for the natural value of thecosmological constant when the bulk has two large extra dimensions and the bulksupersymmetry is partially preserved (or completely broken).

Bulk Renormalization and Particle Spectrum in Codimension-Two Brane Worlds