Correlation functions and spectral curves in models of minimal gravity

TL;DR

This paper investigates correlation functions in minimal gravity models, proposing an algorithm for calculating invariant ratios and verifying the spectral curve hypothesis, bridging quasiclassical hierarchy and Liouville theory.

Contribution

It introduces a new algorithm for computing invariant ratios and confirms the exact spectral curve form in minimal gravity models.

Findings

Algorithm for invariant ratios calculation

Verification of spectral curve hypothesis

Transition coefficient between bases established

Abstract

The correlation functions for models of minimal gravity are discussed. An algorithm is proposed for calculations of invariant ratios from formulas of residues that can be compared with the coefficients of expansion of the partition function in Liouville theory. For (2,2K-1) models transition coefficient from basis of quasiclassical hierarchy to basis Liouville theory is obtained evidently, and the hypothesis about exact form of spectral curve has been verified.