Boundary timelike Liouville theory: bulk 1-point & boundary 2-point functions

TL;DR

This paper derives bulk one-point and boundary two-point functions in boundary timelike Liouville theory using bootstrap, revealing they are not simple analytic continuations of spacelike versions.

Contribution

It provides the first explicit bootstrap derivation of structure constants in boundary timelike Liouville theory, highlighting their distinct nature from spacelike cases.

Findings

Structure constants are not analytic continuations of spacelike counterparts.

Explicit formulas for bulk one-point functions.

Explicit formulas for boundary two-point functions.

Abstract

We consider timelike Liouville theory with FZZT-like boundary conditions. The bulk one-point and boundary two-point structure constants on a disk are derived using bootstrap. We find that these structure constants are not the analytic continuations of their spacelike counterparts.