Correlation Functions and Vertex Operators of Liouville Theory

TL;DR

This paper computes correlation functions for vertex operators in Liouville theory, extending known results and exploring their relation to the Liouville S-matrix, with implications for understanding the theory's structure.

Contribution

It provides explicit calculations of correlation functions for negative integer exponential vertex operators and develops integral representations for general cases.

Findings

Correlation functions for specific vertex operators are explicitly calculated.

Conditional validity of Dorn and Otto's conjectures is demonstrated.

Connections between vertex operator structures and the Liouville S-matrix are identified.

Abstract

We calculate correlation functions for vertex operators with negative integer exponentials of a periodic Liouville field, and derive the general case by continuing them as distributions. The path-integral based conjectures of Dorn and Otto prove to be conditionally valid only. We formulate integral representations for the generic vertex operators and indicate structures which are related to the Liouville S-matrix.