Cut-and-Join operator representation for Kontsevich-Witten tau-function

TL;DR

This paper presents a straightforward cut-and-join operator formulation for the Kontsevich-Witten tau-function, derived from Virasoro constraints, with potential applications in topological gravity.

Contribution

It introduces a novel, simple operator representation for the tau-function of 2D topological gravity based on Virasoro constraints.

Findings

Derived a cut-and-join operator expression for the tau-function

Connected the operator form to Virasoro constraints

Discussed potential applications in topological gravity

Abstract

In this short note we construct a simple cut-and-join operator representation for Kontsevich-Witten tau-function that is the partition function of the two-dimensional topological gravity. Our derivation is based on the Virasoro constraints. Possible applications of the obtained expression are discussed.