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 sig ma 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 oscillatio ns in four transverse dimensions 'intrinsic' to the black hole: four n on-compact directions of the D = 5 black hole case and three non-compa ct and one compact (responsible for embedding of magnetic charges) dim ensions in the D = 4 black hole case, Oscillations in other compact in ternal dimensions give subleading contributions to statistical entropy in the limit when all charges are large. The dominant term in the sta tistical entropy is thus universal (i.e. is the same in type II and he terotic string theory) and agrees with the Bekenstein-Hawking expressi on.