Topological String on AdS_3 x N

TL;DR

This paper explores the topological string theory on AdS_3 x N, demonstrating the emergence of a topological conformal algebra in space-time from world-sheet topological structures, and relating it to known N=2 superconformal theories.

Contribution

It constructs the space-time topological conformal algebra directly from world-sheet topological theory and extends the formulation beyond the boundary region.

Findings

Space-time conformal algebra is topological and derived from world-sheet theory.

The approach uses Wakimoto free field representation near the boundary.

A more rigid formulation of the space-time topological algebra is presented.

Abstract

We study the topologically twisted string theory on the general back-ground $AdS_3\times {\cal N}$ 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).