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We discuss an exact false vacuum decay rate at one loop for a real andcomplex scalar field in a quartic-quartic potential with two tree-level minima.The bounce solution is used to compute the functional determinant from bothfluctuations. We obtain the finite product of eigenvalues and removetranslational zero modes. The orbital modes are regularized with the zetafunction and we end up with a complete renormalized decay rate. We derivesimple expansions in the thin and thick wall limits and determine theirvalidity.

Exact one-loop false vacuum decay rate