Quantum fusion of strings (flux tubes) and domain walls

We consider formation of composite strings and domain walls as a result of fusion of two elementary objects (elementary strings in the first case and elementary walls in the second) located at a distance from each other. The tension of the composite object T2 is assumed to be less than twice the tension of the elementary object T1, so that bound states are possible. If in the initial state the distance d between the fusing strings or walls is much larger than their thickness and satisfies the conditions T1d2 1 (in the string case) and T1d3 1 (in the wall case), the problem can be fully solved quasiclassically. The fusion probability is determined by the first, "under the barrier" stage of the process. We find the bounce configuration and its extremal action SB. In the wall problem e-SB gives the fusion probability per unit time per unit area. In the string case, due to a logarithmic infrared divergence, the problem is well formulated only for finite-length strings. The fusion probability per unit time can be found in the limit in which the string length is much larger than the distance between two merging strings.