Conformal and Quasiconformal Realizations¶of Exceptional Lie Groups

By M. Günaydin, Kilian Koepsell, H. Nicolai. 2000

166 citations recorded by the source corpus.

Abstract: We present a nonlinear realization of E8(8) on a space of 57 dimensions, which is quasiconformal in the sense that it leaves invariant a suitably defined “light cone” in ℝ57. This realization, which is related to the Freudenthal triple system associated with the unique exceptional Jordan algebra over the split octonions, contains previous conformal realizations of the lower rank exceptional Lie groups on generalized space times, and in particular a conformal realization of E7(7) on ℝ27 which we exhibit explicitly. Possible applications of our results to supergravity and M-Theory are briefly mentioned.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1f894406dcd7ad7430247e3ee2f0cce4cb2bd9ef

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. D. Thompson
2. David S. Berman
3. M. Cederwall
4. B. Pioline
5. John C. Baez
6. D. Marqués
7. O. Hohm
8. C. Nuñez

In Nuclear and High Energy Physics

1. D. Thompson
2. David S. Berman
3. Sergio Ferrara
4. M. Cederwall
5. B. Pioline
6. John C. Baez
7. Axel Kleinschmidt
8. Alessio Marrani

In Statistical and Nonlinear Physics

1. D. Thompson
2. David S. Berman
3. M. Cederwall
4. Sergio Ferrara
5. B. Pioline
6. John C. Baez
7. Axel Kleinschmidt
8. D. Marqués

Citations in the corpus

• The gauge structure of generalised diffeomorphisms (2012, background): “For n = 7, the grading corresponding to E8(8) ⊃ E7(7) × SL(2,R) is a 5-grading [66].”
• The Octonions (2001, background): “Murat Günaydin [48] has extended this to a relation between 10-dimensional conformal geometry and E7(−25), and in work with Kilian Koepsell and Hermann Nikolai [49] has explicated how this is connected to Freudenthal triple systems.”
• Lectures on black holes, topological strings and quantum attractors (2006, background): “These considerations lend support to the idea that the three-dimensional U-duality group should play a rôle as a spectrum-generating symmetry for 4-dimensional black holes [149, 143, 159, 48].”
• Charge Orbits of Symmetric Special Geometries and Attractors (2006, background): “Under dimensional reduction to d = 4, such a correspondence gets extended to a correspondence between the field strengths of the vector fields (and their magnetic duals) and the Freudenthal triple system (FTS) [57, 46] F (J ) defined over J [37, 3, 1, 4, 7], and it can be realized as 2× 2 “matrices””
• Black Holes, Qubits and Octonions (2008, unknown): “3) was established in [154, 155].”