Topological String on AdS 3 ×N

We study the topologically twisted string theory on the general back-ground AdS3× N which is compatible with the world-sheet N = 2 superconformal symmetry and is extensively discussed in the recent works [20]. 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 [11]. 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 [20].