Correlation Functions and Multicritical Flows in $c<1$ String Theory

TL;DR

This paper computes all tree-level correlation functions in $c<1$ string theory using the ring structure, explores multicritical behavior via perturbations, and connects different models through these perturbations, aligning with matrix model results.

Contribution

It provides a comprehensive calculation of correlation functions and demonstrates how multicritical models can be derived from simpler models through perturbations.

Findings

Correlation functions are computed explicitly for $c<1$ string theory.

Multicritical models are obtained from basic models via perturbations.

Results align with known matrix model outcomes.

Abstract

We compute all string tree level correlation functions of vertex operators in $c<1$ string theory. This is done by using the ring structure of the theory. In order to study the multicritical behaviour, we calculate the correlation functions after perturbation by physical vertex operators. We show that the $(2k-1,2)$ models can be obtained from the $(1,2)$ model and the minimal models can be obtained from the $(1,p)$ model by perturbing the action by appropriate physical operators. Our results are consistent with known results from matrix models.