On the Non-renormalization of the AdS Radius

TL;DR

This paper demonstrates that the AdS radius remains unrenormalized at one-loop in superstring theory, confirming the stability of the AdS/CFT correspondence at this order through explicit quantum calculations.

Contribution

It provides a proof that the AdS radius is not renormalized at one-loop by computing the quantum effective action and showing the absence of finite alpha' corrections.

Findings

No finite alpha' corrections to the effective action.

The central charge vanishes at one-loop.

The AdS radius remains stable at one-loop.

Abstract

We show that the relation between the 't Hooft coupling and the radius of AdS is not renormalized at one-loop in the sigma model perturbation theory. We prove this by computing the quantum effective action for the superstring on AdS_5 x S^5 and showing that it does not receive any finite alpha' corrections. We also show that the central charge of the interacting worldsheet conformal field theory vanishes at one-loop.