2005/06/30 by Boris Pioline
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #hep-th
paper · pdf · doi:10.1088/1126-6708/2005/08/071
published as JHEP 0508 (2005) 071 · 36 pages, uses JHEP3.cls; v5: the "extra charge", which was, mistakenly identified as angular momentum, is now correctly identified as NUT charge (see historical note on p29), a few other cosmetic changes too
openalex publication_date 2005/08/23 · arxiv created 2005/12/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We discuss the degeneracies of 4D and 5D BPS black holes in toroidal compactifications of M-theory or type II string theory, using U-duality as a tool. We generalize the 4D/5D lift to include all charges in N=8 supergravity, and compute the exact indexed degeneracies of certain 4D 1/8-BPS black holes. Using the attractor formalism, we obtain the leading micro-canonical entropy for arbitrary Legendre invariant prepotentials and non-vanishing D6-brane charge. In particular, we find that the N=8 prepotential is given to leading order by the cubic invariant of E6. This suggests that the minimal unitary representation of E8, based on the same cubic prepotential, underlies the microscopic degeneracies of N=8 black holes. We propose that the exact degeneracies are given by the Wigner function of the E8(Z) invariant vector in this automorphic representation. A similar conjecture relates the degeneracies of N=4 black holes to the minimal unipotent representation of SO(8,24,Z).