Path integral formulation of Hodge duality on the brane

TL;DR

This paper uses path integral formulation to clarify how Hodge duality operates on the brane in warped compactifications, resolving a puzzle about the binding of scalar and tensor fields.

Contribution

It provides a path integral approach to implement Hodge duality in warped compactifications, clarifying the prescription by Duff and Liu.

Findings

Hodge duality can be consistently implemented via path integrals in warped backgrounds.

The Duff and Liu prescription is naturally explained within this framework.

Scalar fields can be bound to the brane, but higher-rank tensors require careful treatment.

Abstract

In the warped compactification with a single Randall-Sundrum brane, a puzzling claim has been made that scalar fields can be bound to the brane but their Hodge dual higher-rank anti-symmetric tensors cannot. By explicitly requiring the Hodge duality, a prescription to resolve this puzzle was recently proposed by Duff and Liu. In this note, we implement the Hodge duality via path integral formulation in the presence of the background gravity fields of warped compactifications. It is shown that the prescription of Duff and Liu can be naturally understood within this framework.