TY - JOUR

T1 - Black holes admitting a Freudenthal dual

AU - Borsten, L.

AU - Dahanayake, D.

AU - Duff, M. J.

AU - Rubens, W.

PY - 2009/8/6

Y1 - 2009/8/6

N2 - The quantized 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 Δ(x) determines the lowest-order entropy. Here, we introduce a Freudenthal duality x→x, for which x=-x. Although distinct from U duality, it nevertheless leaves Δ(x) invariant. However, the requirement that x be an integer restricts us to the subset of black holes for which Δ(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 quantized 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.

AB - The quantized 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 Δ(x) determines the lowest-order entropy. Here, we introduce a Freudenthal duality x→x, for which x=-x. Although distinct from U duality, it nevertheless leaves Δ(x) invariant. However, the requirement that x be an integer restricts us to the subset of black holes for which Δ(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 quantized 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.

UR - http://www.scopus.com/inward/record.url?scp=69249159860&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.80.026003

DO - 10.1103/PhysRevD.80.026003

M3 - Article

AN - SCOPUS:69249159860

SN - 1550-7998

VL - 80

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 2

M1 - 026003

ER -