Probing AdS/CFT correspondence via world-sheet methods and 2d gravity like scaling arguments

TL;DR

This paper uses world-sheet methods and 2d gravity scaling arguments to understand features of the AdS_3/CFT_2 correspondence, proposing a stringy perturbation approach that connects 2d CFTs to AdS_3 string theory.

Contribution

It introduces a string-based perturbation framework for 2d CFTs that elucidates the AdS_3/CFT_2 correspondence through scale and symmetry considerations.

Findings

Perturbation of 2d CFTs leads to finite-dimensional space-time symmetries.

A specific perturbation yields string theory on AdS_3.

The scale in the theory corresponds to the AdS radial coordinate.

Abstract

We show how some features of the AdS/CFT correspondence for AdS_3 can easily be understood via standard world-sheet methods and 2d gravity like scaling arguments. To do this, we propose a stringy way for perturbing two-dimensional CFT's around their critical points. Our strategy is to start from a stringy (world-sheet) representation of 2d CFT in space-time. Next we perturb a world-sheet action by some marginal operators such that the space-time symmetry becomes finite dimensional. As a result, we get a massive FT in space-time with a scale provided by two-dimensional coupling constant. It turns out that there exists a perturbation that leads to string theory on AdS_3. In this case the scale is equivalently provided by the radial anti-de-Sitter coordinate.