On the timelike Liouville three-point function

Abstract

In a recent paper, D. Harlow, J. Maltz, and E. Witten showed that a particular proposal for the timelike Liouville three-point function, originally due to Al. Zamolodchikov and to I. Kostov and V. 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.

11 pages. v2 comments and references added. Appropriate credit is given to Ref. arXiv:hep-th/0512346, where the Coulomb gas computation of the c<1 theory has already been discussed

References in corpus (4)

• Analytic Continuation of Liouville Theory
• A Holographic Framework for Eternal Inflation
• Notes on Liouville Theory at c<=1
• Non-Rational 2D Quantum Gravity II. Target Space CFT

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