The end of the road for bulk fields in warped Randall–Sundrum braneworlds

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 $$L(F)=b\sqrt{F}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>L</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>F</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>b</mml:mi> <mml:msqrt> <mml:mi>F</mml:mi> </mml:msqrt> </mml:mrow> </mml:math> admits a consistent and normalizable zero mode, and that among $$p-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>-</mml:mo> </mml:mrow> </mml:math> forms, consistency occurs solely for the free $$0-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>-</mml:mo> </mml:mrow> </mml:math> 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.