The End of the Road for Bulk Fields in Braneworlds

TL;DR

This paper establishes universal local consistency conditions for bulk fields in arbitrary-dimensional braneworlds, revealing that only certain free fields are compatible and providing a no-go theorem for fermions and many gauge fields.

Contribution

It derives the first fully local, dimension-independent criteria for bulk fields, generalizing previous results and establishing broad constraints on field propagation in braneworld models.

Findings

Free scalar fields are consistent and localized.

Maxwell fields generally violate the conditions, leading to a no-go theorem.

Only specific nonlinear electrodynamics models admit zero modes.

Abstract

In this manuscript we generalize Ref. [1] and derive a complete set of local consistency conditions for bulk fields in braneworld scenarios with an arbitrary number of dimensions. This provides the first fully local and dimension-independent generalization of all known criteria for bulk fields. Within this framework, we show that a free scalar field is consistent and localized, whereas minimally and non-minimally coupled Maxwell fields violate the conditions, leading to a no-go theorem valid in any dimension. For nonlinear electrodynamics, we find that only the model $L(F)=b\sqrt{F}$ admits a consistent and normalizable zero mode, and that among p-forms, consistency occurs solely for the free 0-form. We also demonstrate that Dirac fermions, with or without Yukawa terms, are inconsistent within this framework and therefore cannot propagate in the bulk. Our local approach makes explicit that these conclusions do not depend on any particular internal geometry or warp factor: previously known results arise merely as special cases of a broader and strictly local structure, highlighting the universality of the constraints derived here.