Exceptional geometry and Borcherds superalgebras

Abstract

We study generalized diffeomorphisms in exceptional geometry with U-duality group E_{n(n)} from an algebraic point of view. By extending the Lie algebra e_n to an infinite-dimensional Borcherds superalgebra, involving also the extension to e_{n+1}, the generalized Lie derivatives can be expressed in a simple way, and the expressions take the same form for any n less than 8. The closure of the transformations then follows from the Jacobi identity and the grading of e_{n+1} with respect to e_n.

19 pages. v2: Changes in the part of section 3.3 about generalized Jordan triple systems. v3: Typos corrected. Published version. v4: Infinitesimal changes

References in corpus (15)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Generalised Geometry for M-Theory
• Generalized Geometry and M theory
• Exceptional Field Theory III: E${}_{8(8)}$
• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• The E_{11} origin of all maximal supergravities
• E(11) and the Embedding Tensor
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• Kac-Moody Spectrum of (Half-)Maximal Supergravities
• Superalgebras, constraints and partition functions
• Three-Algebras in N = 5, 6 Superconformal Chern-Simons Theories: Representations and Relations
• Generalised Space-time and Gauge Transformations
• Forms and algebras in (half-)maximal supergravity theories
• Monopoles, three-algebras and ABJM theories with $\mathbb{N}=5,6,8$ supersymmetry

Cited by in corpus (20)

• Exceptional field theory: $SL(5)$
• Exceptional field theory: $SO(5,5)$
• Loops in exceptional field theory
• Generalised diffeomorphisms for E${}_9$
• Beyond E11
• Extended geometries
• $L_{\infty }$ algebras for extended geometry from Borcherds superalgebras
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• Tensor hierarchy algebras and extended geometry I: Construction of the algebra
• Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras
• Infinity-enhancing of Leibniz algebras
• Teleparallelism in the algebraic approach to extended geometry
• SL(5) supersymmetry
• Extended geometry of magical supergravities
• The teleparallel complex
• Unfolding $E_{11}$
• $L_{\infty }$ algebras for extended geometry
• Pre-NQ Manifolds and Correspondence Spaces: the Nilmanifold Example
• Algebraic structures in exceptional geometry
• Generators and relations for (generalised) Cartan type superalgebras