Vacuum interaction of conic singularities

In the $(\operatorname{tr}\ln)$-formalism, we consider the problem of the vacuum interaction of conic singularities in a $D$-dimensional ($D\ge 3$) space–time. We show that the interaction energy regularized by dimensional regularization contains neither ultraviolet divergences nor divergences associated with the nonintegrable nature of the vacuum mean of the energy–momentum tensor operator. In the case of four space–time dimensions, the result coincides with those obtained previously in a local approach.