Standard 4-D gravity on a brane in six dimensional flux compactifications

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We consider a six-dimensional space-time, in which two of the dimensions are compactified by a flux. Matter can be localized on a codimension one brane coupled to the bulk gauge field and wrapped around an axis of symmetry of the internal space. By studying the linear perturbations around this background, we show that the gravitational interaction between sources on the brane is described by Einstein 4d gravity at large distances. Our model provides a consistent setup for the study of gravity in a football compactification, without having to deal with the complications of a delta–like, codimension two brane. Moreover, it allows us to identify the origin of the problems that emerge when one takes the limit of a codimension-two brane.