2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220394We review on a recent construction of the on-shell supersymmetric brane action for the codimension-two branes with nonzero tension in the flux compactification of a 6D chiral gauged supergravity. On dimesionally reducing on 4D gauged supergravity for a new supersymmetric unwarped background with conical branes, we consider the modulus stabilization for determining the soft masses of the scalars localized on the branes and show that the bulk U(1)_R provides a new mechanism for mediating the SUSY breaking.12 pages, no figures, Invited review for Modern Physics Letters A, Published versionHigh Energy Physics - Theorytext