Entropy of the Schwarzschild black hole and the string–black-hole correspondence

The string–black-hole correspondence is considered in the context of the correspondence principle proposed recently by Horowitz and Polchinski. We demonstrate that the entropy of string states and the entropy of a Schwarzschild black hole can be matched including the subleading terms which depend on mass logarithmically. We argue the necessity to include the string interaction (with coupling $g)$ in the consideration and propose the $g^2$-dependent modification of the string entropy. The matching of it with the entropy of the Schwarzschild black hole is analyzed. We also discuss a possible scenario when the entropy of a Schwarzschild black hole appears entirely as an effect of the interaction.