Arithmetic of N=8 Black Holes

Understand

The microscopic formula for the degeneracies of 1/8 BPS black holes in type II string theory compactified on a six dimensional torus can be expressed as a sum of several terms.

• One of the terms is a function of the Cremmer-Julia invariant and gives the leading contribution to the entropy in the large charge limit.
• The other terms, which give exponentially subleading contribution, depend not only on the Cremmer-Julia invariant, but also on the arithmetic properties of the charges, and in fact exist only when the charges satisfy special arithmetic properties.
• We identify the origin of these terms in the macroscopic formula for the black hole entropy, based on quantum entropy function, as the contribution from non-trivial saddle point(s) in the path integral of string theory over the near horizon geometry.