  We study the problem of self-energy of pointlike charges in higher
dimensional static spacetimes. Their energy, as a functional of the spacetime
metric, is invariant under a specific continuous transformation of the metric.
We show that the procedure of regularization of this formally divergent
functional breaks this symmetry and results in an anomalous contribution to the
finite renormalized self-energy. We proposed a method of calculation of this
anomaly and presented an explicit expressions for it in the case of a scalar
charge in four and five-dimensional static spacetimes. This anomalous
correction proves to be zero in even dimensions, but it does not vanish in
odd-dimensional spacetimes.
