Observations on Arithmetic Invariants and U-Duality Orbits in N =8 Supergravity
arXiv:0912.0057 · doi:10.1007/JHEP03(2010)081
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.
27 p, minor corrections, version published in JHEP
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- The Ultraviolet Finiteness of N=8 Supergravity
- Freudenthal Dual Lagrangians
- Jordan C*-Algebras and Supergravity
- Exceptional Reductions
- Iwasawa N=8 Attractors
- Pair Production of small Black Holes in Heterotic String Theories
- Perturbative higher-derivative terms in N=6 asymmetric orbifolds
- Real weights, bound states and duality orbits
- Mock modularity at work, or black holes in a forest
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- Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories
- Perturbative and Non-Perturbative Aspects of N=8 Supergravity