Duality in Black Holes

Hawking revealed that black holes have an extraordinarily high entropy, and he (using a work by Bekenstein) showed that the entropy is proportional to the area of the event horizon. But where does this entropy come from? What are its microscopic ingredients? My colleague Andy Strominger and I were able to get an exact solution for the entropy, or internal degrees of freedom, of a black hole using a dual description in string theory. The string theory calculation involved counting the number of spheres–around which membranes, or “D-branes,” are wrapped–that can fit inside a 6-dimensional Calabi-Yau manifold. This approach yielded the same answer as the Bekenstein-Hawking formula, while offering a detailed internal picture that showed how black holes could have such high entropies. This was a notable achievement for string theory as well as a testament to the power of dualities: counting mathematical objects inside a Calabi-Yau miraculously gave the same number as that deduced from the horizon area of a black hole.