K(E9) from K(E10)

Abstract

We analyse the M-theoretic generalisation of the tangent space structure group after reduction of the D=11 supergravity theory to two space-time dimensions in the context of hidden Kac-Moody symmetries. The action of the resulting infinite-dimensional `R symmetry' group K(E9) on certain unfaithful, finite-dimensional spinor representations inherited from K(E10) is studied. We explain in detail how these representations are related to certain finite codimension ideals within K(E9), which we exhibit explicitly, and how the known, as well as new finite-dimensional `generalised holonomy groups' arise as quotients of K(E9) by these ideals. In terms of the loop algebra realisations of E9 and K(E9) on the fields of maximal supergravity in two space-time dimensions, these quotients are shown to correspond to (generalised) evaluation maps, in agreement with previous results of Nicolai and Samtleben (hep-th/0407055). The outstanding question is now whether the related unfaithful representations of K(E10) can be understood in a similar way.

35 pages; v2: References added; v3: Author, one reference and two appendices added. Extended results in sections 3.2 and 4.2

References in corpus (24)

• E_11 and M Theory
• E10 and a "small tension expansion" of M Theory
• Dualisation of Dualities, I
• Hidden Superconformal Symmetry in M Theory
• Very Extended $E_8$ and $A_8$ at low levels, Gravity and Supergravity
• The IIA, IIB and eleven dimensional theories and their common E_{11} origin
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• Hidden symmetries and the fermionic sector of eleven-dimensional supergravity
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• E10 and SO(9,9) invariant supergravity
• Extended E8 Invariance of 11-Dimensional Supergravity
• K(E10), Supergravity and Fermions
• Massive IIA Supergravity as a Non-linear Realisation
• IIB supergravity and E10
• Integrability and Canonical Structure of d=2, N=16 Supergravity
• Hidden Symmetries and Dirac Fermions
• Gradient Representations and Affine Structures in AE(n)
• Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity Theories
• IIA and IIB spinors from K(E10)
• The topology of U-duality (sub-)groups
• Generalized holonomy of M-theory vacua
• Pure type I supergravity and DE(10)

Cited by in corpus (14)

• Spacelike Singularities and Hidden Symmetries of Gravity
• Beyond E11
• Gauging hidden symmetries in two dimensions
• Constraints and the E10 Coset Model
• Beyond the standard model with six-dimensional spinors
• On higher spin realizations of K(E10)
• Representations of involutory subalgebras of affine Kac-Moody algebras
• Real forms of extended Kac-Moody symmetries and higher spin gauge theories
• Sugawara-type constraints in hyperbolic coset models
• The E10 Wheeler-DeWitt operator at low levels
• The massless irreducible representation in E theory and how bosons can appear as spinors
• The teleparallel complex
• Generalised holonomies and K(E${}_9$)
• The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces