Dilaton-Axion Wormhole Partition Function Away from the BPS Endpoint

Abstract

I determine the leading finite-radius correction to the two-boundary response of a charged axion wormhole near its BPS endpoint. With $δ=a_*^2$, exact radial matching in a product axion--dilaton/saxion system gives a boundary eigenvalue that vanishes as $O(δ)$ and an off-diagonal Hessian entry of order $O(δ^2)$. Their combination produces a cross-boundary covariance linear in $δ$, with a negative first sub-leading correction on the branch studied here. I determine the semiclassical range in which the quadratic approximation remains controlled and identify the first finite-radius angular resonance, $δ^2\log(δ/δ_0)$. Under a uniform rescaling of all active charges, the coefficient of the linear cross-boundary response scales as the inverse square of the charge scale. I then average the inverse response over the chiral Gaussian ensemble describing the BPS endpoint. Boundary reduction preserves the hard-edge index. Multiplication by the matched BPS sector weight converts the normalized response into the leading finite-radius two-source coefficient.