Heuristic expectation of DOZZ vanishing at the Seiberg bound

Ascertain whether heuristic or semiclassical arguments in genus-0 Liouville theory should lead one to expect that the DOZZ three-point function vanishes when any Liouville momentum α_i reaches the Seiberg bound Q/2 (with Q = b + 1/b).

Background

The paper analyzes Liouville theory correlators using rigorous probabilistic methods and compares the resulting insights with the DOZZ formula for the genus-0 three-point function. After integrating over the Liouville zero-mode, the authors identify an extended region of convergence bounded by nonperturbative phenomena, and they discuss how certain ultraviolet effects manifest as poles of the DOZZ formula.

Surprisingly, the authors highlight a third boundary of this region where the DOZZ formula exhibits a zero rather than a pole, specifically when one of the Liouville momenta reaches the Seiberg bound α = Q/2. They provide a probabilistic explanation for the vanishing but note that it is not clear whether standard heuristic reasoning should have predicted this outcome. Clarifying this would bridge the rigorous probabilistic approach with conventional heuristic or semiclassical expectations in Liouville theory.