Motivated by recent progress on the correspondence between string theory on anti-de Sitter space and conformal field theory, we address the question of constructing space-time N-extended superconformal algebras (SCAs) on the boundary of AdS₃. Based on a free field realization of an affine SL(2|N/2) current superalgebra residing on the world sheet, the Virasoro generators and the N supercurrents may be constructed explicitly. The resulting SCA has an affine SL(N/2) x U(1) Kac-Moody algebra as an internal subalgebra. An interesting property of the construction is that for N>2 it treats the supercurrents in an asymmetric way. Thus, we are witnessing a new class of SCAs not obtainable by conventional hamiltonian reduction. Particular attention is paid to the case N=4 where the resulting SCA is a new and asymmetric N=4 SCA. The algebra is shown to be invariant under a linear twist of the generators except for a unique value of the continuous twist the generators except for a unique value of the continuous twist parameter. At this value, the invariance is broken and the algebra collapses to the well-known small N=4 SCA. It should be stressed that despite the title and anticipated applications to string theory, this work may be viewed as a purely algebraic study in conformal field theory.

Tuesday, June 27th 2000, 13:00
Ernest Rutherford Physics Building, room 326