José Figueroa-O'Farrill (Edinburgh):
Supergravity
Vacua and Plücker Relations
I will report on work in progress in collaboration with Ali
Chamseddine and Wafic Sabra at CAMS (Beirut). I will present a
classification of maximally supersymmetric solutions of chiral
(1,0) supergravity in six dimensions. They are given by certain
Lie groups with a bi-invariant lorentzian metric. The solutions
are shown to be related by Penrose limits, which in this case are
group contractions. As a byproduct we obtain a characterisation
of manifolds admitting a certain type of flat metric connection
with torsion. If time allows I will try to contrast this with
recent work in collaboration with George Papadopoulos on
ten-dimensional IIB supergravity and to some mysterious
Pluecker-like relations which appear there.