Extremal black hole entropy from conformal string sigma model

We present a string-theory derivation of the semiclassical entropy of extremal dyonic black holes in the approach based on the conformal sigma model (NS-NS embedding of the classical solution). We demonstrate (resolving some puzzles existing in previous related discussions) that the degeneracy responsible for the entropy is due to string oscillations in four transverse dimensions 'intrinsic' to the black hole: four non-compact directions of the D = 5 black hole case and three non-compact and one compact (responsible for embedding of magnetic charges) dimensions in the D = 4 black hole case, Oscillations in other compact internal dimensions give subleading contributions to statistical entropy in the limit when all charges are large. The dominant term in the statistical entropy is thus universal (i.e. is the same in type II and heterotic string theory) and agrees with the Bekenstein-Hawking expression.