E10 and the BKL limit of M theory

by Hermann Nicolai (MPI Potsdam)

Tuesday 7 Oct 2003, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

A formal "small tension" expansion of D = 11 supergravity near a spacelike singularity is shown to be equivalent, at least up to 30th order in height, to a null geodesic motion in the infinite dimensional coset space E10/K(E10) where K(E10) is the maximal compact subgroup of the hyperbolic Kac-Moody group E10(R). The proof makes use of a novel decomposition of E10 into irreducible representations of its SL(10,R) subgroup, whose structure has been determined explicitly up to level 28. It is shown how to identify the first four rungs of the E10 coset fields with the values of geometric quantities constructed from D=11 supergravity fields and their spatial gradients at some comoving spatial point.