A relation between $(2,2m-1)$ minimal strings and the Virasoro minimal string

TL;DR

This paper establishes a connection between Virasoro minimal strings and $(2,2m-1)$ minimal strings, using matrix models to derive string equations and analyze correlators and quantum volumes in the JT gravity limit.

Contribution

It introduces a new formulation of Virasoro minimal strings via matrix models, enabling computation of correlators and analysis of their scaling behavior.

Findings

Derived the string equation for Virasoro minimal strings from density of states expansion.

Connected Virasoro minimal strings to multicritical matrix models dual to $(2,2m-1)$ minimal strings.

Analyzed the scaling behavior of correlators and quantum volumes in the JT gravity limit.

Abstract

We propose a connection between the newly formulated Virasoro minimal string and the well-established $(2,2m-1)$ minimal string by deriving the string equation of the Virasoro minimal string using the expansion of its density of states in powers of $E^{m+1/2}$. This string equation is expressed as a power series involving double-scaled multicritical matrix models, which are dual to $(2,2m-1)$ minimal strings. This reformulation of Virasoro minimal strings enables us to employ matrix theory tools to compute its $n$-boundary correlators. We analyze the scaling behavior of $n$-boundary correlators and quantum volumes $V^{(b)}_{0,n}(\ell_1,\dots,\ell_n)$ in the JT gravity limit.