  We 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.
