The AdS3 central charge in string theory

Understand

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.