Boundary operators and touching of loops in 2d gravity

TL;DR

This paper explores the role of boundary operators and loop interactions in 2D gravity by analyzing correlators in minimal conformal models coupled to gravity using the two-matrix model.

Contribution

It establishes simple fusion rules for all scaling operators and clarifies the connection between boundary operators and loop touching phenomena.

Findings

Fusion rules for scaling operators are simple and universal.

Boundary operators are crucial in understanding loop touching.

The two-matrix model effectively captures boundary effects in 2D gravity.

Abstract

We investigate the correlators in unitary minimal conformal models coupled to two-dimensional gravity from the two-matrix model. We show that simple fusion rules for all of the scaling operators exist. We demonstrate the role played by the boundary operators and discuss its connection to how loops touch each other.