Timelike Liouville three-point function

Abstract

In a recent paper, Harlow, Maltz, and Witten showed that a particular proposal for the timelike Liouville three-point function, originally due to Zamolodchikov and to Kostov and Petkova, can actually be computed by the original Liouville path integral evaluated on a new integration cycle. Here, we discuss a Coulomb gas computation of the timelike three-point function and show that an analytic extension of the Selberg-type integral formulas involved reproduces the same expression, including the adequate normalization. A notable difference with the spacelike calculation is pointed out. © 2012 American Physical Society.