10D N=1 MASSLESS BPS SUPERMULTIPLETS

We consider d=10, N=1 supersymmetry algebra with maximal number of tensor charges Z and introduce a class of orbits of Z, invariant w.r.t. the T8 subgroup of massless particles' little group T8⋉ SO (8). For that class of orbits we classify all possible orbits and little groups, which appear to be semidirect products T8⋉ SO (k1)×⋯× SO (kn), with k1+⋯+kn=8, where compact factor is embedded into SO (8) by triality map. We define actions of little groups on supercharge Q and construct corresponding supermultiplets. In some particular cases we show the existence of supermultiplets with both Fermi and Bose sectors consisting of the same representations of tensorial Poincaré. In addition, complete classification of supermultiplets (not restricted to T8-invariant orbits) with rank-2 matrix of supersymmetry charges anticommutator, is given.

The Normality in Products with a Countably Compact Factor

It is known that the product ω1 × X of ω1 with an M1-spacemay be nonnormal. In this paper we prove that the product κ × X of an uncountable regular cardinal κ with a paracompact semi-stratifiable space is normal iff it is countably paracompact. We also give a sufficient condition under which the product of a normal space with a paracompact space is normal, from which many theorems involving such a product with a countably compact factor can be derived.