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We analyze the fluctuations of Nielsen-Olesen vortices arising in thesix-dimensional Abelian-Higgs model. The regular geometry generated by thedefect breaks spontaneously six-dimensional Poincar\'e symmetry leading to awarped space-time with finite four-dimensional Planck mass. As a consequence,the zero mode of the spin two fluctuations of the geometry is always localizedbut the graviphoton fields, corresponding to spin one metric fluctuations, giverise to zero modes which are not localized either because of their behaviour atinfinity or because of their behaviour near the core of the vortex. A similarsituation occurs for spin zero fluctuations. Gauge field fluctuations exhibit alocalized zero mode.Comment: 45 pages in Revtex style with 4 figure

Zero modes of six-dimensional Abelian vortices