We apply Borel resummation method to the conventional perturbation series of ground state energy in a metastable potential, V (x) = x 2 /2 − gx 4 /4. We observe numerically that the discontinuity of Borel transform reproduces the imaginary part of energy eigenvalue, i.e., total decay width due to the quantum tunneling.The agreement with the exact numerical value is remarkable in the whole tunneling regime 0 < g < 0.7.

We present a direct field theoretical calculation of the consistent gauge anomaly in the superfield formalism, on the basis of a definition of the effective action through the covariant gauge current. The scheme is conceptually and technically simple and the gauge covariance in intermediate steps reduces calculational labors considerably. The resultant superfield anomaly, being proportional to the anomaly d abc = tr T a {T b , T c }, is minimal without supplementing any counterterms. Our anomaly coincides with the anomaly obtained by Marinković as the solution of the Wess-Zumino consistency condition.⋆

On the basis of Borel resummation, we propose a systematical improvement of bounce calculus of quantum bubble nucleation rate. We study a metastable super-with an attractive interaction. The validity of our proposal is tested in D = 1 (quantum mechanics) by using the perturbation series of ground state energy to high orders. We also present a result in D = 2, based on an explicit calculation of vacuum bubble diagrams to five loop orders.

An imaginary part of the false-vacuum energy density in a metastable system, i.e., the decay width due to quantum tunneling, might be reproduced by Borel resummation of vacuum bubble diagrams. We examine the convergence of this prescription in the Gaussian propagator model, in which the analytical expression of vacuum bubbles to the ninth order of loop expansion is available.