Curvature corrections to the low energy effective theory in 6D regularized braneworlds

TL;DR

This paper investigates second order curvature corrections in the low energy effective gravitational theory on a 6D flux compactified braneworld, revealing divergences in the metric as the brane becomes infinitesimally thin.

Contribution

It extends previous analyses by including second order corrections and analyzing their effects in a 6D Einstein-Maxwell braneworld model.

Findings

Standard 4D Einstein gravity is recovered at lowest order.

Second order corrections involve quadratic energy-momentum tensors.

Divergences occur in the metric in the thin-brane limit.

Abstract

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.