BPS black hole degeneracies and minimal automorphic representations
Jun, 200532 pages
Published in:
- JHEP 08 (2005) 071
e-Print:
- hep-th/0506228 [hep-th]
Report number:
- LPTHE-05-15,
- LPTENS-05-20
Citations per year
Abstract:
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 . This suggests that the minimal unitary representation of , 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 invariant vector in this automorphic representation. A similar conjecture relates the degeneracies of N=4 black holes to the minimal unipotent representation of .- M-theory
- higher-dimensional
- compactification: torus
- string model
- effective action
- U-duality
- soliton: BPS
- charge: topological
- charge: fractional
- black hole
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