Casimir-Robin Backreaction between Positive Anti-de Sitter (AdS4) Branes: A Semiclassical No-Go for a Static Five-Dimensional Wormhole

Abstract

This preprint investigates the semiclassical backreaction generated by the Casimir effect for massless conformally coupled scalar fields confined between two positive AdS4 branes with local Robin boundary conditions in a five-dimensional Einstein-gravity background. The detuned AdS4/AdS5 seed geometry admits an exact conformal reduction to H4 x I, allowing the finite interbrane Casimir interaction, Robin spectral properties, surface stress-energy, and homogeneous semiclassical backreaction to be computed self-consistently. For a reference effective field theory realization with positive constant Robin coefficients, the resulting configuration is a regular and stable five-dimensional vacuum with a positive Robin spectral gap, controlled curvature invariants, and a stable radion. Although the Casimir stress violates the five-dimensional null energy condition along directions involving the extra dimension, its leading radial null contraction vanishes. An exact geometric analysis shows that the homogeneous warped-AdS4 branch admits no stationary spherically symmetric throat. In addition, effective-field-theory power counting shows that the radial quantum corrections required to support a localized throat become relevant only when the semiclassical control parameter approaches order unity, where the low-energy approximation loses predictive control. The main result is therefore a semiclassical no-go statement for a static spherically symmetric traversable wormhole within the controlled constant-Robin, two-positive-brane sector. The model nevertheless provides a self-consistent example of a regular five-dimensional Casimir vacuum with directional negative-energy effects.