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

Understand

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.