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

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.

Figures (3)

• Figure 1: String equation \ref{['eq:stringeq_complete']} for different values of $b$. It is shown that the solution to the string equation is $x(0)=0$ for all $0<b\leq 1$.
• Figure 2: Logaritmic behavior of the times $t_m$ in \ref{['eq:stringeq_complete']}. As $b\rightarrow 0$, the slower they decrease with respect to $m$.
• Figure 3: String equation \ref{['eq:stringeq_complete']} for different values of $b$ in the regime $u<0$.