Topological string on AdS(3) x N

We study the topologically twisted string theory on the general back-ground AdS(3) x N which is compatible with the world-sheet N = 2 superconformal s ymmetry and is extensively discussed in the recent works [28]. After summar izing the algebraic structure of the world-sheet topological theory, we sho w that the space-time (boundary) conformal theory should be also topologica l. We directly construct the space-time topological conformal algebra (twis ted N = 2 superconformal algebra) from the degrees of freedom in the world- sheet topological theory. Firstly, we work on the world-sheet of the string propagating near boundary, in which we can safely make use of the Wakimoto free field representation. Secondly, we present a more rigid formulation o f space-time topological conformal algebra which is still valid far from th e boundary along the line of [18]. We also discuss about the relation betwe en this space-time topological theory and the twisted version of the space- time N = 2 superconformal field theory given in [28]. (C) 2000 Elsevier Sci ence B.V. All rights reserved.