English

Observations on Arithmetic Invariants and U-Duality Orbits in N =8 Supergravity

High Energy Physics - Theory 2010-06-25 v2

Abstract

We establish a relation between time-like, light-like and space-like orbits of the non-compact E{7(7)}(R)symmetry and discrete E{7(7)}(Z) invariants. We discuss the U-duality invariant formula for the degeneracy of states d(Q) which in the approximation of large occupation numbers reproduces the Bekenstein-Hawking entropy formula for regular black holes with AdS_2 horizon. We explain why the states belonging to light-like orbits, corresponding to classical solutions of "light black holes with null singularity", decouple from the corresponding index. We also present a separate U-duality invariant formula for the class of light-like orbits specified by discrete E{7(7)}(Z) invariants. We conclude that the present study of the non-perturbative sector of the theory does not reveal any contradiction with the conjectured all-loop perturbative finiteness of D=4 N=8 supergravity.

Keywords

Cite

@article{arxiv.0912.0057,
  title  = {Observations on Arithmetic Invariants and U-Duality Orbits in N =8 Supergravity},
  author = {Massimo Bianchi and Sergio Ferrara and Renata Kallosh},
  journal= {arXiv preprint arXiv:0912.0057},
  year   = {2010}
}

Comments

27 p, minor corrections, version published in JHEP

R2 v1 2026-06-21T14:17:59.974Z