BPS black hole degeneracies and minimal automorphic representations

Jun, 2005
32 pages
Published in:
  • JHEP 08 (2005) 071
e-Print:
Report number:
  • LPTHE-05-15,
  • LPTENS-05-20

Citations per year

200520102015202020240246810
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 E6E_6. This suggests that the minimal unitary representation of E8E_8, 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)E_8(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)SO(8,24,Z).
  • M-theory
  • higher-dimensional
  • compactification: torus
  • string model
  • effective action
  • U-duality
  • soliton: BPS
  • charge: topological
  • charge: fractional
  • black hole