Abstract
We study the topologically twisted string theory on the general back-ground AdS 3× N which is compatible with the world-sheet N=2 superconformal symmetry and is extensively discussed in the recent works [? ]. After summarizing the algebraic structure of the world-sheet topological theory, we show that the space–time (boundary) conformal theory should be also topological. We directly construct the space–time topological conformal algebra (twisted 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 of space–time topological conformal algebra which is still valid far from the boundary along the line of [? ]. We also discuss about the relation between this space–time topological theory and the twisted version of the space–time N=2 superconformal field theory given in [? ].
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