  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.

High Energy Physics - Theory