Twisted String Theory in Anti-de Sitter Space

TL;DR

This paper develops a topologically twisted string theory in three-dimensional anti-de Sitter space, revealing how boundary energy-momentum becomes topological under certain symmetry twists, advancing understanding of quantum gravity in AdS.

Contribution

It introduces a boundary-metric independent, topologically twisted string theory in AdS3 with N=2 superconformal symmetry, and derives the corresponding boundary energy-momentum vertex operator.

Findings

Boundary energy-momentum tensor becomes topological after U(1) R-symmetry twist.

Constructed world sheet vertex operator encodes boundary energy-momentum.

Demonstrated independence from boundary metric in the topologically twisted theory.

Abstract

We construct a string theory in three-dimensional anti-de Sitter space-time that is independent of the boundary metric. It is a topologically twisted theory of quantum gravity. We study string theories with an asymptotic N=2 superconformal symmetry and demonstrate that, when the world sheet coupling to the space-time boundary metric undergoes a U(1) R-symmetry twist, the space-time boundary energy-momentum tensor becomes topological. As a by-product of our analysis, we obtain the world sheet vertex operator that codes the space-time energy-momentum for conformally flat boundary metrics.