Forms and algebras in (half-)maximal supergravity theories
arXiv:1503.00015 · doi:10.1007/JHEP05(2015)032
Abstract
The forms in D-dimensional (half-)maximal supergravity theories are discussed for 3 D 11. Superspace methods are used to derive consistent sets of Bianchi identities for all the forms for all degrees, and to show that they are soluble and fully compatible with supersymmetry. The Bianchi identities determine Lie superalgebras that can be extended to Borcherds superalgebras of a special type. It is shown that any Borcherds superalgebra of this type gives the same form spectrum, up to an arbitrary degree, as an associated Kac-Moody algebra. For maximal supergravity up to D-form potentials, this is the very extended Kac-Moody algebra E11. It is also shown how gauging can be carried out in a simple fashion by deforming the Bianchi identities by means of a new algebraic element related to the embedding tensor. In this case the appropriate extension of the form algebra is a truncated version of the so-called tensor hierarchy algebra.
arXiv comment59 pages, 1 figure
References in corpus (62)
- E_11 and M Theory
- Eleven Dimensional Origin of String/String Duality: A One Loop Test
- The Dirichlet Super-p-Branes in Ten-Dimensional Type IIA and IIB Supergravity
- E10 and a "small tension expansion" of M Theory
- Dualisation of Dualities, I
- On Lagrangians and Gaugings of Maximal Supergravities
- Maximal gauged supergravity in three dimensions
- Dualisation of Dualities, II: Twisted self-duality of doubled fields and superdualities
- Gauged maximal supergravities and hierarchies of nonabelian vector-tensor systems
- ICTP Lectures on Covariant Quantization of the Superstring
- Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions
- The E_{11} origin of all maximal supergravities
- Fibre Bundles and Generalised Dimensional Reduction
- D=10, N=IIB Supergravity: Lorentz-invariant actions and duality
- E(11) and the Embedding Tensor
- New supergravities with central charges and Killing spinors in 2+1 dimensions
- Gauged locally supersymmetric D=3 nonlinear sigma models
- Off-shell supergravity-matter couplings in three dimensions
- Spinorial cohomology and maximally supersymmetric theories
- IIB Supergravity Revisited
- Component Actions from Curved Superspace: Normal Coordinates and Ectoplasm
- N=8 matter coupled AdS_3 supergravities
- Supergravities without an Action: Gauging the Trombone
- Weyl Superspace
- Borcherds symmetries in M-theory
- A New Massive Type IIA Supergravity From Compactification
- E(11)-extended spacetime and gauged supergravities
- Kac-Moody Spectrum of (Half-)Maximal Supergravities
- IIA Ten-forms and the Gauge Algebras of Maximal Supergravity Theories
- Duality in Supergravity Theories
- The tensor hierarchy algebra
- Gauging Maximal Supergravities
- Superdualities, Brane Tensions and Massive IIA/IIB Duality
- On higher-order corrections in M theory
- The E(11) origin of all maximal supergravities - the hierarchy of field-strengths
- IIA/IIB Supergravity and Ten-forms
- Tensor hierarchies, Borcherds algebras and E11
- The tensor hierarchy simplified
- Real Borcherds Superalgebras and M-theory
- Gauged Supergravities in Various Spacetime Dimensions
- Maximal supergravity in three dimensions: supergeometry and differential forms
- Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra
- The cohomology of superspace, pure spinors and invariant integrals
- Half-maximal supergravity in three dimensions: supergeometry, differential forms and algebraic structure
- D=3, N=8 conformal supergravity and the Dragon window
- Supersymmetry algebra cohomology III: Primitive elements in four and five dimensions
- Maximal supergravity in D=10: forms, Borcherds algebras and superspace cohomology
- Kappa-symmetric SL(2,R) covariant D-brane actions
- E10 and Gauged Maximal Supergravity
- Local E(11) and the gauging of the trombone symmetry
- Supersymmetry algebra cohomology II: Primitive elements in 2 and 3 dimensions
- Homology of Lie algebra of supersymmetries
- , Borcherds algebras and maximal supergravity
- Supersymmetry algebra cohomology IV: Primitive elements in all dimensions from D=4 to D=11
- Oxidizing Borcherds symmetries
- Supersymmetry algebra cohomology I: Definition and general structure
- Heterotic supergeometry revisited
- Superspace formulations of ten-dimensional supergravity
- Maximal Nine Dimensional Supergravity, General gaugings and the Embedding Tensor
- Notophs of N = 8 supergravity
- Borcherds and Kac-Moody extensions of simple finite-dimensional Lie algebras
- Kac-Moody and Borcherds Symmetries of Six-Dimensional Chiral Supergravity
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- Beyond E11
- Superalgebras, constraints and partition functions
- Exceptional geometry and Borcherds superalgebras
- E Exceptional Field Theory in Superspace
- Tensor hierarchy algebras and extended geometry I: Construction of the algebra
- Chern-Simons Actions and Their Gaugings in 4D, N=1 Superspace
- Generators and relations for Lie superalgebras of Cartan type
- Symmetries of M-theory and free Lie superalgebras
- Exceptional field theories, superparticles in an enlarged 11D superspace and higher spin theories
- All Chern-Simons Invariants of 4D, N = 1 Gauged Superform Hierarchies
- Type II Double Field Theory in Superspace
- On section conditions of E7(7) exceptional field theory and superparticle in N=8 central charge superspace
- Notophs of N = 8 supergravity
- Exotic branes and mixed-symmetry potentials I: predictions from symmetry