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The End of the Road for Bulk Fields in Braneworlds

G. Alencar, R. S. Almeida, R. N. Costa Filho, T. M. Crispim, Francisco S. N. Lobo

TL;DR

The paper presents a fully local, dimension-agnostic framework of consistency conditions for bulk fields in braneworlds, derived from the coupled gravity–field dynamics without fixing the warp factor or internal geometry. By formulating four local constraints (CCI–CCIV) on the bulk energy–momentum tensor and applying them to scalars, bosons, nonlinear electrodynamics, and fermions, it establishes broad no-go theorems for field localization: only free scalars can be consistently localized, while Maxwell fields, most p-forms, Dirac fermions, and many nonlinear electrodynamics models are excluded. A unique exception arises for nonlinear electrodynamics with L(F)=b√F, which can admit a localizable zero mode independent of dimensionality; all other nonlinear deformations of Maxwell theory fail to meet the local conditions. The results hold universally across arbitrary spacetime dimensions and internal geometries, refining the landscape of viable braneworld models and informing future studies on gravity–matter coupling, potential higher-derivative or scalar-tensor extensions, and localized nonlinear phenomena on branes.

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.

The End of the Road for Bulk Fields in Braneworlds

TL;DR

The paper presents a fully local, dimension-agnostic framework of consistency conditions for bulk fields in braneworlds, derived from the coupled gravity–field dynamics without fixing the warp factor or internal geometry. By formulating four local constraints (CCI–CCIV) on the bulk energy–momentum tensor and applying them to scalars, bosons, nonlinear electrodynamics, and fermions, it establishes broad no-go theorems for field localization: only free scalars can be consistently localized, while Maxwell fields, most p-forms, Dirac fermions, and many nonlinear electrodynamics models are excluded. A unique exception arises for nonlinear electrodynamics with L(F)=b√F, which can admit a localizable zero mode independent of dimensionality; all other nonlinear deformations of Maxwell theory fail to meet the local conditions. The results hold universally across arbitrary spacetime dimensions and internal geometries, refining the landscape of viable braneworld models and informing future studies on gravity–matter coupling, potential higher-derivative or scalar-tensor extensions, and localized nonlinear phenomena on branes.

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 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.
Paper Structure (17 sections, 107 equations)

This paper contains 17 sections, 107 equations.

Table of Contents

  1. Introduction
  2. Review of braneworld consistency conditions
  3. Global Sum Rules
  4. Duff et al. consistency condition
  5. Generalization of Duff et al. consistency condition
  6. Alencar et al. Local Sum Rules
  7. Generalization of Gibbons et al. consistency condition in arbitrary dimensions
  8. Local sum rules for bulk fields in arbitrary dimensions
  9. Background solution
  10. Consequences for bulk fields
  11. Aplications on bulk fields
  12. Scalar field
  13. Bosonic fields
  14. Fermionic fields
  15. Spinors in odd-dimensional spacetimes, $D=2k+3$
  16. ...and 2 more sections