Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-03-31
Phys.Rev.D80:026003,2009
Physics
High Energy Physics
High Energy Physics - Theory
32 pages revtex, 10 tables; minor corrections, references added
Scientific paper
10.1103/PhysRevD.80.026003
The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm Delta(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the requirement that \tilde{x} be integer restricts us to the subset of black holes for which Delta(x) is necessarily a perfect square. The issue of higher-order corrections remains open as some, but not all, of the discrete U-duality invariants are Freudenthal invariant. Similarly, the quantised charges A of five dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm N(A) determines the lowest order entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a perfect cube, for which A**=A and which leaves N(A) invariant. The two dualities are related by a 4D/5D lift.
Borsten L.
Dahanayake D.
Duff M. J.
Rubens W.
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