Reevaluation of a Mixed Point-Splitting Contraction in "Lessons on Eternal Traversable Wormholes in AdS"

This technical note reexamines the mixed-derivative contraction appearing in the point-splitting evaluation of the stress-energy tensor in "Lessons on Eternal Traversable Wormholes in AdS" (JHEP 07 (2019) 122). Direct differentiation of the reported propagator correction yields a nonvanishing bulk contribution. The residual is derived for general spacetime dimension D > 3 and shown to cancel the explicit z-dependence of the corresponding bulk T_zz. In D = 4, the reevaluated normal component is 3/2 times the published midpoint result, whereas in D = 5 the ratio is 7/6. The conformal improvement term leaves the bulk T_zz unchanged under the assumed translational symmetries while restoring the expected trace relation. The result is restricted to the bulk point-splitting contribution and does not constitute a complete renormalization of the boundary-coupled theory or a universal correction to the original model.