Localizing Gauge Fields on a Topological Abelian String and the Coulomb Law

Abstract

The confinement of electromagnetic field is studied in axial symmetrical, warped, 6D World Brane, using a recently proposed topological abelian string vortex solution as background. It was found, that the massless gauge field fluctuations follow 4D Maxwell equations in the Lorenz gauge. The massless zero mode is localized when the thickness of the string-vortex is less than 5% $\beta /4\pi e^2$ there are not others localized massless modes. There is also an infinite of non localized massive Fourier modes, that follow 4 dimensional Proca equations with a continuous spectrum. To compute the corrections to the Coulomb potential, a radial cutoff was introduced, in order to achieve a discrete mass spectrum. As main result, a $\frac{1}{R^2}$ correction was found for the 4D effective Coulomb law. Although, this correction is milder than the expected for flat 5+1 dimensional electromagnetism, the result is in correspondence with the observed behavior of the Coulomb potential at nowadays measurable distances.

15pages, 3 figures

References in corpus (3)

• Higher order corrections to the Newtonian potential in the Randall-Sundrum model
• Gauge field localization on brane worlds
• Inflating branes inside abelian strings

Cited by in corpus (8)

• Bounds on topological Abelian string-vortex and string-cigar from information-entropic measure
• Localization and mass spectrum of $q-$form fields on branes
• Exotic Elko on String-Like Defects in Six Dimensions
• A 6D standing-wave Braneworld with normal matter as source
• Consistency Conditions for Fields Localization on Braneworlds
• Kaluza-Klein modes of $U(1)$ gauge vector field on brane with codimension-$d$
• Refinements of the Weyl pure geometrical thick branes from information-entropic measure
• The End of the Road for Bulk Fields in Warped Randall-Sundrum Braneworlds