Magic Coset Decompositions
arXiv:1201.6314
Abstract
By exploiting a "mixed" non-symmetric Freudenthal-Rozenfeld-Tits magic square, two types of coset decompositions are analyzed for the non-compact special Kähler symmetric rank-3 coset E7(-25)/[(E6(-78) x U(1))/Z_3], occurring in supergravity as the vector multiplets' scalar manifold in N=2, D=4 exceptional Maxwell-Einstein theory. The first decomposition exhibits maximal manifest covariance, whereas the second (triality-symmetric) one is of Iwasawa type, with maximal SO(8) covariance. Generalizations to conformal non-compact, real forms of non-degenerate, simple groups "of type E7" are presented for both classes of coset parametrizations, and relations to rank-3 simple Euclidean Jordan algebras and normed trialities over division algebras are also discussed.
34 pages, 1 figure, 7 tables; Improved presentation
References in corpus (17)
- Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry
- Four-qubit entanglement from string theory
- On the Nature of the Phase Transition in SU(N), Sp(2) and E(7) Yang-Mills theory
- Black holes admitting a Freudenthal dual
- Orbits and Attractors for N=2 Maxwell-Einstein Supergravity Theories in Five Dimensions
- Exceptional Lie groups
- Magic Supergravities, N= 8 and Black Hole Composites
- d=4 Attractors, Effective Horizon Radius and Fake Supergravity
- On the Black-Hole/Qubit Correspondence
- Non-BPS Attractors in 5d and 6d Extended Supergravity
- Freudenthal Duality and Generalized Special Geometry
- Two-Center Black Holes Duality-Invariants for stu Model and its lower-rank Descendants
- Mapping the geometry of the E6 group
- Exceptional Groups and Physics
- Black Hole Nilpotent Orbits and Tits Satake Universality Classes
- Attractors and first order formalism in five dimensions revisited
- Hopf maps and Wigner's little groups