alpha'-exact entropies for BPS and non-BPS extremal dyonic black holes   in heterotic string theory from ten-dimensional supersymmetry
  We calculate near-horizon solutions for four-dimensional 4-charge and five-dimensional 3-charge black holes in heterotic string theory from the part of the ten-dimensional tree-level effective action which is connected to gravitational Chern-Simons term by supersymmetry. We obtain that the entropies of large black holes exactly match the alpha'-exact statistical entropies obtained from microstate counting (D=4) and AdS/CFT correspondence (D=5). Especially interesting is that we obtain agreement for both BPS and non-BPS black holes, contrary to the case of R^2-truncated (four-derivative) actions (D-dimensional N=2 off-shell supersymmetric or Gauss-Bonnet) were used, which give the entropies agreeing (at best) just for BPS black holes. The key property of the solutions, which enabled us to tackle the action containing infinite number of terms, is vanishing of the Riemann tensor \bar{R}_{MNPQ} obtained from torsional connection defined with \bar{\Gamma} = \Gamma - H/2. Morover, if every monomial of the remaining part of the effective action would contain at least two Riemanns \bar{R}_{MNPQ}, it would trivially follow that our solutions are exact solutions of the full heterotic effective action in D=10. The above conjecture, which appeared (in this or stronger form) from time to time in the literature, has controversial status, but is supported by the most recent calculations of Richards (arXiv:0807.3453 [hep-th]). Agreement of our results for the entropies with the microscopic ones supports the conjecture. As for small black holes, our solutions in D=5 still have singular horizons. 
Predrag Dominis Prester and Tomislav Terzic