Puncture Operator in c=1 Liouville Gravity

TL;DR

This paper identifies the puncture operator in c=1 Liouville gravity as a discrete state with spin J=1/2 and derives recursion relations for correlation functions involving this operator.

Contribution

It establishes the puncture operator as a specific discrete state and derives recursion relations for correlation functions using operator product expansion.

Findings

Correlation functions satisfy topological gravity recursion relations

Recursion relations allow computation of multi-point functions from fewer points

Puncture operator identified as discrete state with spin J=1/2

Abstract

We identify the puncture operator in c=1 Liouville gravity as the discrete state with spin J=1/2. The correlation functions involving this operator satisfy the recursion relation which is characteristic in topological gravity. We derive the recursion relation involving the puncture operator by the operator product expansion. Multiple point correlation functions are determined recursively from fewer point functions by this recursion relation.