False vacuum decay: Effective one-loop action for pair creation of domain walls

Abstract

An effective one-loop action built from the soliton field itself for the two-dimensional (2D) problem of soliton pair creation is proposed. The action consists of the usual mass term and a kinetic term in which the simple derivative of the soliton field is replaced by a covariant derivative. In this effective action the soliton charge is treated no longer as a topological charge but as a Noether charge. Using this effective one-loop action, the soliton–antisoliton pair production rate Γ/L=A exp[−S0] is calculated and one recovers Stone’s exponential factor S0 and the prefactor A of Kiselev, Selivanov, and Voloshin. The results are also valid straightforwardly to the problem of pair creation rate of domain walls in dimensions D⩾3.