Tensor hierarchies, Borcherds algebras and E11

Abstract

Gauge deformations of maximal supergravity in D=11-n dimensions generically give rise to a tensor hierarchy of p-form fields that transform in specific representations of the global symmetry group E(n). We derive the formulas defining the hierarchy from a Borcherds superalgebra corresponding to E(n). This explains why the E(n) representations in the tensor hierarchies also appear in the level decomposition of the Borcherds superalgebra. We show that the indefinite Kac-Moody algebra E(11) can be used equivalently to determine these representations, up to p=D, and for arbitrarily large p if E(11) is replaced by E(r) with sufficiently large rank r.

22 pages. v2: Published version (except for a few minor typos detected after the proofreading, which are now corrected)

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Cited by in corpus (26)

• The gauge structure of generalised diffeomorphisms
• Half-maximal supersymmetry from exceptional field theory
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• The tensor hierarchy algebra
• Beyond E11
• The tensor hierarchy simplified
• Supersymmetric Domain Walls
• Superalgebras, constraints and partition functions
• Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
• Exceptional geometry and Borcherds superalgebras
• Half-maximal supergravity in three dimensions: supergeometry, differential forms and algebraic structure
• Towards an M5-Brane Model II: Metric String Structures
• Forms and algebras in (half-)maximal supergravity theories
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Locally non-geometric fluxes and missing momenta in M-theory
• Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras
• Infinity-enhancing of Leibniz algebras
• Generators and relations for Lie superalgebras of Cartan type
• Symmetries of M-theory and free Lie superalgebras
• Oxidizing Borcherds symmetries
• SL(5) supersymmetry
• Unfolding $E_{11}$
• Exotic branes and mixed-symmetry potentials I: predictions from $E_{11}$ symmetry
• Borcherds and Kac-Moody extensions of simple finite-dimensional Lie algebras
• $E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies
• A study on free roots of Borcherds-Kac-Moody Lie Superalgebras