Hodge Duality on the Brane

TL;DR

This paper clarifies how Hodge duality is preserved on the brane in Randall-Sundrum models by demonstrating the correct reduction of bulk p-form potentials and discusses the implications for photon screening phenomena.

Contribution

It resolves the apparent contradiction in p-form field localization by showing the correct duality correspondence on the brane.

Findings

A 3-form in the bulk yields a 2-form on the brane consistent with duality.

Photon screening in Randall-Sundrum geometry is ruled out by Einstein equations.

The duality between bulk and brane fields is maintained as expected.

Abstract

It has been claimed that whereas scalars can be bound to a Randall-Sundrum brane, higher p-form potentials cannot, in contradiction with the Hodge duality between 0-form and 3-form potentials in the five-dimensional bulk. Here we show that a 3-form in the bulk correctly yields a 2-form on the brane, in complete agreement with both bulk and brane duality. We also emphasize that the phenomenon of photon screening in the Randall-Sundrum geometry is ruled out by the bulk Einstein equation.