Conformal and Quasiconformal Realizations of Exceptional Lie Groups

Abstract

We present a nonlinear realization of E_8 on a space of 57 dimensions, which is quasiconformal in the sense that it leaves invariant a suitably defined ``light cone'' in 57 dimensions. 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 E_7 on a 27 dimensional vector space which we exhibit explicitly. Possible applications of our results to supergravity and M-Theory are briefly mentioned.

21 pages, 1 figure. Revised version. Connection between SU(8) and SL(8,R) bases clarified; formulas corrected; references added

Cited by in corpus (76)

• The gauge structure of generalised diffeomorphisms
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• Charge Orbits of Symmetric Special Geometries and Attractors
• Universal BPS structure of stationary supergravity solutions
• Black Holes, Qubits and Octonions
• Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
• On N=8 attractors
• Strings, Black Holes, and Quantum Information
• Supergravities without an Action: Gauging the Trombone
• Magic Supergravities, N= 8 and Black Hole Composites
• Twistors and Black Holes
• Black holes in N=8 supergravity from SO(4,4) hidden symmetries
• Minimal representations, spherical vectors, and exceptional theta series I
• $R^4$ couplings and automorphic unipotent representations
• E_7 and the tripartite entanglement of seven qubits
• Quantum Attractor Flows
• BPS Black Hole Degeneracies and Minimal Automorphic Representations
• Topological wave functions and heat equations
• Three-Qubit Operators, the Split Cayley Hexagon of Order Two and Black Holes
• Generalized spacetimes defined by cubic forms and the minimal unitary realizations of their quasiconformal groups
• Exceptional F(4) Higher-Spin Theory in AdS(6) at One-Loop and other Tests of Duality
• Explicit Action of E7(7) on N=8 Supergravity Fields
• Octonionic black holes
• Gravity as the square of Yang-Mills?
• Unitary Realizations of U-duality Groups as Conformal and Quasiconformal Groups and Extremal Black Holes of Supergravity Theories
• Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions
• Invariant Differential Operators for Non-Compact Lie Algebras Parabolically Related to Conformal Lie Algebras
• Super Yang-Mills, division algebras and triality
• Quasi-conformal actions, quaternionic discrete series and twistors: SU(2,1) and G_2(2)
• Global symmetries of Yang-Mills squared in various dimensions
• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
• A Unified Approach to the Minimal Unitary Realizations of Noncompact Groups and Supergroups
• Spectrum Generating Conformal and Quasiconformal U-Duality Groups, Supergravity and Spherical Vectors
• Deformed Twistors and Higher Spin Conformal (Super-)Algebras in Six Dimensions
• New E77 invariants and amplitudes
• 5D Black Holes and Non-linear Sigma Models
• Freudenthal Dual Lagrangians
• Exceptional Lie Algebras, SU(3) and Jordan Pairs Part 2: Zorn-type Representations
• $E_8$, the most exceptional group
• Freudenthal Gauge Theory
• Lectures on Spectrum Generating Symmetries and U-duality in Supergravity, Extremal Black Holes, Quantum Attractors and Harmonic Superspace
• U-duality covariant membranes
• On duality symmetry in perturbative quantum theory
• Exceptional Lie Algebra $E_{7(-25)}$ (Multiplets and Invariant Differential Operators)
• Superconformal M2-branes and generalized Jordan triple systems
• Minimal unitary representation of SO*(8) = SO(6,2) and its SU(2) deformations as massless 6D conformal fields and their supersymmetric extensions
• M-theory Cosmology, Octonions, Error Correcting Codes
• Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
• Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems
• Jordan Pairs, E6 and U-Duality in Five Dimensions
• Harmonic Superspace, Minimal Unitary Representations and Quasiconformal Groups
• Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8
• The Geometry of Exceptional Super Yang-Mills Theories
• Minimal unitary representation of D(2,1;λ) and its SU(2) deformations and d=1, N=4 superconformal models
• SU(2) deformations of the minimal unitary representation of OSp(8*|2N) as massless 6D conformal supermultiplets
• Generalized conformal realizations of Kac-Moody algebras
• A Kind of Magic
• The Magic of Being Exceptional
• Orbits in Non-Supersymmetric Magic Theories
• Non-Supersymmetric Magic Theories and Ehlers Truncations
• Real weights, bound states and duality orbits
• Classification of simple linearly compact Kantor triple systems over the complex numbers
• The supersymmetric black holes of N=8 supergravity
• Towards Massless Sector of Tensionless Strings on $Ad{S}_5$
• Minimal representations and reductive dual pairs in conformal field theory
• $E_{7(7)}$ invariant non-extremal entropy
• Multi-Centered Invariants, Plethysm and Grassmannians
• Development of a unified tensor calculus for the exceptional Lie algebras
• On Dimensional Reduction of Magical Supergravity Theories
• Collineation groups of octonionic and split-octonionic planes
• On an Algebraic Structure of Dimensionally Reduced Magical Supergravity Theories
• Jordan Algebraic Interpretation of Maximal Parabolic Subalgebras : Exceptional Lie Algebras
• BPS Black Hole Entropy and Attractors in Very Special Geometry. Cubic Forms, Gradient Maps and their Inversion
• Nonlinear realisations of Lie superalgebras
• Vinberg's T-Algebras. From Exceptional Periodicity to Black Hole Entropy
• Flipped $SU(5)$ GUT with conformal gravity from a single supermultiplet