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 on the boundary of
AdS_3. Based on a free field realization of an affine SL(2|N/2) current
superalgebra residing on the world sheet, we construct explicitly the Virasoro
generators and the N supercurrents. N is even. The resulting superconformal
algebra has an affine SL(N/2) \otimes U(1) current algebra as an internal
subalgebra. Though we do not complete the general superalgebra, we outline the
underlying construction and present supporting evidence for its validity.
Particular attention is paid to its BRST invariance. In the classical limit
where the free field realization may be substituted by a differential operator
realization, we discuss further classes of generators needed in the closure of
the algebra. We find sets of half-integer spin fields, and for N>4 these
include generators of negative weights. 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 superconformal algebras not obtainable
by conventional Hamiltonian reduction. The complete classical algebra is
provided in the case N=4 and is of a new and asymmetric form.Comment: 29 pages, LaTeX, extends hep-th/990518
