  We derive a closed-form false vacuum decay rate at one loop in the thin wall
limit, where the true and false vacua are nearly degenerate. We obtain the
bounce configuration in $D$ dimensions, together with the Euclidean action with
a higher order correction, counter-terms and renormalization group running. We
extract the functional determinant via the Gel'fand-Yaglom theorem for low and
generic orbital multipoles. The negative and zero eigenvalues appear for low
multipoles and the translational zeroes are removed. We compute the
fluctuations for generic multipoles, multiply and regulate the orbital modes.
We find an explicit finite renormalized decay rate in $D = 3, 4$ and give a
closed-form expression for the finite functional determinant in any dimension.
