The rate of metastable vacuum decay in (2+1) dimensions

The pre-exponential factor in the probability of decay of a metastable vacuum is calculated for a generic (2+1) dimensional model in the limit of small difference $\epsilon$ of the energy density between the metastable and the stable vacua. It is shown that this factor is proportional to $\epsilon^{-7/3}$ and that the power does not depend on details of the underlying field theory. The calculation is done by using the effective Lagrangian method for the relevant soft (Goldstone) degrees of freedom in the problem. Unlike in the (1+1) dimensional case, where the decay rate is completely determined by the parameters of the effective Lagrangian and is thus insensitive to the specific details of the underlying (microscopic) theory, in the considered here (2+1) dimensional case the pre-exponential factor is found up to a constant, which does depend on specifics of the underlying short-distance dynamics, but does not depend on the energy asymmetry parameter $\epsilon$. Thus the functional dependence of the decay rate on $\epsilon$ is universally determined in the considered limit of small $\epsilon$.