$(2,2p+1)$ minimal string and intersection theory I

TL;DR

This paper reexamines the $(2,2p+1)$ minimal string, revealing a new link between correlation numbers and $p$-deformed volumes, and deriving intersection-theoretic formulas to connect worldsheet and matrix model approaches.

Contribution

It introduces a novel identification between correlation numbers and $p$-deformed volumes, providing new formulas and equations for minimal string theory.

Findings

Identified a link between correlation numbers and $p$-deformed volumes.

Derived intersection-theoretic formulas for correlation numbers.

Established recurrent equations analogous to Virasoro minimal string.

Abstract

In view of recent progress in studying matrix model-2D gravity duality, we reexamine some features of $(2,2p+1)$ minimal string. After reviewing both sides of the proposed correspondence in this case, a previously unnoted identification between correlation numbers of tachyon operators in certain domain of parameter space and "$p$-deformed volumes", which are certain integral transforms of topological recursion data, is described and clarified. This identification allows us to efficiently study correlation numbers at finite matter central charge. In particular, we obtain an intersection-theoretic formula and the simplest recurrent equations for them, analogous to the ones recently derived for Virasoro minimal string. These formulas might be useful in establishing a more thorough connection between worldsheet and matrix model approaches.