String-loop corrected magnetic black holes

We discuss the form of the string-loop-corrected effective action obtained by compactification of the heterotic string theory on the manifold K3xT2 or on its orbifold limit and the loop-corrected solutions of the equations of motion. Effective 4D theory has N=2 locally supersymmetry. Using the string-loop-corrected prepotential of N=2 supersymmetric theory, which receives corrections only from the string world sheets of torus topology, we calculate the loop corrections to the tree-level effective action and solve the loop-corrected equations of motion. At the string-tree level, a solution that we consider is the extremal magnetic black hole in which case the tree-level effective gauge couplings decrease at small distances from the origin, and in this region string-loop corrections to the gauge couplings become important. (author)