On mini-superspace limit of boundary three-point function in Liouville field theory

TL;DR

This paper investigates the mini-superspace semiclassical limit of boundary three-point functions in Liouville field theory, demonstrating an exact match with Morse potential quantum mechanics matrix elements, both expressed via hypergeometric functions.

Contribution

It establishes a precise correspondence between Liouville boundary three-point functions and Morse potential quantum mechanics in the mini-superspace limit, with explicit hypergeometric function representations.

Findings

Exact agreement between boundary three-point functions and Morse matrix elements.

Both functions are expressed using generalized hypergeometric functions.

Provides insights into the semiclassical limit of Liouville theory.

Abstract

We study mini-superspace semiclassical limit of the boundary three-point function in the Liouville field theory. We compute also matrix elements for the Morse potential quantum mechanics. An exact agreement between the former and the latter is found. We show that both of them are given by the generalized hypergeometric functions.