  We study the effective gravitational theory on a brane in a six-dimensional
Einstein-Maxwell model of flux compactification, regularizing a conical defect
as a codimension-one brane. We employ the gradient expansion technique valid at
low energies. A lowest order analysis showed that standard four-dimensional
Einstein gravity is reproduced on the brane. We extend this study to include
second order corrections in the effective equations, and show that the
correction term is given by a quadratic energy-momentum tensor. Taking the
thin-brane limit where the regularized brane shrinks to the pole, we find that
the second order metric diverges logarithmically on the brane, giving rise to
divergences in the brane effective action. Away from the branes, the effective
action is however well-defined.
