Quantum Vacuum Fluctuations in the Interbrane Bulk and the Insufficiency of Q-balls to Sustain Pentadimensional Wormholes

Abstract

This research provides a rigorous semiclassical analysis of five-dimensional interbrane models within the Randall–Sundrum II framework. The study addresses the energetic stability and physical traversability of Lorentzian wormholes sustained by quantum vacuum fluctuations. The main contributions include: Point-splitting correction: a reevaluation of the mixed contraction of the Euclidean propagator in AdS₅, identifying a finite residual term that increases the negative energy density by a factor of 7/6 relative to the previous literature. Surface energy bound: the application of the minimal covariant completion (ξ = 1/8) to the surface energy-momentum tensor, proving that the energetic cost of the branes (ρΣ) remains positive, thereby acting as a focusing agent. Strong-coupling regime: the derivation of a critical threshold (Ncrit) for the number of quantum fields. The results demonstrate that traversability is a threshold phenomenon; for the standard benchmark (N = 375), the positive surface energy dominates, leading to the collapse of the throat. Physical traversability is recovered only in the strong-coupling domain (N > 377), where the quantum pressure overcomes the brane tension. This work refines the conditions for the existence of traversable wormholes, offering an "honest" and self-consistent model that respects the Ward identity and local energy conservation.