A Correspondence Principle for Black Holes and Strings

TL;DR

The paper introduces a correspondence principle that ties black holes to weakly coupled strings and D-branes, asserting that when the horizon curvature reaches string-scale, the black hole state transitions to a string/D-brane state with the same charges and angular momentum, with mass changing only by a factor of order unity. This framework explains why black hole entropy scales similarly to string/D-brane entropy across neutral, NS-NS, and RR-charged cases in various dimensions and compactifications, though it does not fix numerical coefficients. By analyzing Schwarzschild, NS-charged, and RR-charged solutions, the authors derive consistent entropy matches via horizon-size matching ($r_0^2 \sim \alpha'$) and show how different weak-coupling pictures (long strings, open-string gases on D-branes, and moduli gases) reproduce the correct mass/charge dependence. The results strengthen the view of black holes as ordinary quantum systems in string theory and illuminate how dualities connect seemingly distinct descriptions, while also highlighting where precise coefficients require a deeper understanding of string states at the string scale.

Abstract

For most black holes in string theory, the Schwarzschild radius in string units decreases as the string coupling is reduced. We formulate a correspondence principle, which states that (i) when the size of the horizon drops below the size of a string, the typical black hole state becomes a typical state of strings and D-branes with the same charges, and (ii) the mass does not change abruptly during the transition. This provides a statistical interpretation of black hole entropy. This approach does not yield the numerical coefficient, but gives the correct dependence on mass and charge in a wide range of cases, including neutral black holes.