A doubly covariant formula of deficit angle and its application to six-dimensional braneworld

TL;DR

This paper introduces a doubly covariant boundary condition formulation for axisymmetric codimension-2 braneworlds, enabling more flexible gauge choices and analyzing linear perturbations in six-dimensional warped flux compactifications.

Contribution

It presents a new doubly covariant boundary condition scheme for braneworlds that disentangles bulk and brane coordinates, improving gauge flexibility and applicability to perturbation analysis.

Findings

Boundary conditions are invariant under bulk and brane gauge transformations.

The scheme allows the brane to move freely in the bulk coordinate system.

Application to a six-dimensional model demonstrates the scheme's effectiveness.

Abstract

We reformulate boundary conditions for axisymmetric codimension-2 braneworlds in a way which is applicable to linear perturbation with various gauge conditions. Our interest is in the thin brane limit and thus this scheme assumes that the perturbations are also axisymmetric and that the surface energy-momentum tensor of the brane is proportional to its induced metric. An advantage of our scheme is that it allows much more freedom for convenient coordinate choices than the other methods. This is because in our scheme, the coordinate system in the bulk and that on the brane are completely disentangled. Therefore, the latter does not need to be a subset of the former and the brane does not need to stay at a fixed bulk coordinate position. The boundary condition is manifestly doubly covariant: it is invariant under gauge transformations in the bulk and at the same time covariant under those on the brane. We take advantage of the double covariance when we analyze the linear perturbation of a particular model of six-dimensional braneworld with warped flux compactification.