We reconsider the quantum vacuum interaction energy between two straight parallel cosmic strings. This problem was discussed several times in an approach treating both strings perturbatively and treating only one perturbatively. Here we point out that a simplifying assumption made by Bordag [Ann. Phys. (Berlin) 47, 93 (1990).] can be justified and show that, despite the global character of the background, the perturbative approach delivers a correct result. We consider the applicability of the scattering methods, developed in the past decade for the Casimir effect, for the cosmic string and find it not applicable. We calculate the scattering $T$-operator on one string. Finally, we consider the vacuum interaction of two strings when each carries a two-dimensional delta function potential.

• Received 2 February 2014

DOI:https://doi.org/10.1103/PhysRevD.89.065034