Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-11-28
JHEP 0706:051,2007
Physics
High Energy Physics
High Energy Physics - Theory
35 pages; v2: References added; v3: Author, one reference and two appendices added. Extended results in sections 3.2 and 4.2
Scientific paper
10.1088/1126-6708/2007/06/051
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.
Kleinschmidt Axel
Nicolai Hermann
Palmkvist Jakob
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