Supersymmetric codimension-two branes in six-dimensional gauged supergravity

We consider the six-dimensional Salam-Sezgin supergravity in the presence of codimension-2 branes. In the case that the branes carry only tension, we provide a way to supersymmetrise them by adding appropriate localised Fayet-Iliopoulos terms and modifying accordingly the supersymmetry transformations. The resulting brane action has N = 1 supersymmetry (SUSY). We find the axisymmetric vacua of the system and show that one has unwarped background solutions with football -shaped extra dimensions which always respect N = 1 SUSY, in contrast with the non-supersymmetric brane action background. Finally, we generically find multiple zero modes of the gravitino in this background and discuss how one could obtain a single chiral zero mode present in the low energy spectrum.