Topological String on AdS_3 x N

Abstract

We study the topologically twisted string theory on the general back-ground $Ad{S}_3\times \mathcal{N}$ which is compatible with the world-sheet N=2 superconformal symmetry and is extensively discussed in the recent works (hep-th/9904024, hep-th/9904040). 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 (hep-th/9903219). 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 (hep-th/9904024, hep-th/9904040).

24 pages, typos corrected, the final version to be published in Nucl. Phys. B

References in corpus (2)

• More Comments on String Theory on AdS_3
• Supersymmetric string vacua on AdS_3 x N

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• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• Superconformal Algebras in Light-cone Gauge Quantization of String Theories on $AdS_3