Bulk one-point function on disk in one-matrix model

TL;DR

This paper derives an explicit expression for bulk one-point functions on a disk in the one-matrix model using resonance transformation, aligning with boundary Liouville Field Theory results.

Contribution

It provides a new explicit formula for bulk one-point functions in the one-matrix model, connecting matrix models with Liouville Field Theory.

Findings

Derived explicit bulk one-point function expression.

Confirmed consistency with FZZ boundary Liouville results.

Established link between matrix model and Liouville theory.

Abstract

We consider bulk correlation numbers on disk in one-matrix model. Using the recently found so-called resonance transformation from the KdV to the Liouville frame, we obtain an explicit expression for the bulk one-point function. The result is consistent with the form of FZZ one-point function in the boundary Liouville Field Theory.