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Algebra Seminar
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Vladimir Dobrev
Bulgarian Academy of Sciences

Unitary Irreducible Representations of Noncompact Superalgebras.

Friday 11th October, 12-1pm, Carslaw 373.

Recently, superconformal field theories in various dimensions are attracting great attention due to their applications to superstrings. This makes the classification of the positive energy unitary irreducible representations of the corresponding conformal superalgebras very important. The initial stress was on space-time dimensions D=3,4,5,6 since in these cases the relevant conformal superalgebras satisfy the Haag-Lopuszanski-Sohnius theorem, i.e., the underlying conformal algebra so(D,2) is a simple factor of the bosonic subalgebra. Until recently such classification was known only for the D=4 conformal superalgebras su(2,2/N) by Flato and Fronsdal for N=1 and by Dobrev and Petkova for arbitrary N. This talk will present the general formalism used by D-P and its applications to recent work in the cases D=3,5,6 with stress on the D=6 case, where now the results are complete.