The AdS3 central charge in string theory

TL;DR

This paper calculates the central charge in string theory on AdS3, revealing a finite value consistent with classical gravity after regularization of divergences, and includes string corrections.

Contribution

It provides the first explicit calculation of the vacuum expectation value of the central charge operator in an AdS3 string theory setting.

Findings

Finite one-point function on a spherical worldsheet

Regularization of divergences yields classical gravity value

String corrections modify the central charge value

Abstract

We evaluate the vacuum expectation value of the central charge operator in string theory in an AdS3 vacuum. Our calculation provides a rare non-zero one-point function on a spherical worldsheet. The evaluation involves the regularization both of a worldsheet ultraviolet divergence (associated to the infinite volume of the conformal Killing group), and a space-time infrared divergence (corresponding to the infinite volume of space-time). The two divergences conspire to give a finite result, which is the classical general relativity value for the central charge, corrected in bosonic string theory by an infinite series of tree level higher derivative terms.