Boundary Ground Ring and Disc Correlation Functions in Liouville Quantum Gravity

TL;DR

This paper constructs the boundary ground ring in Liouville quantum gravity with boundary conditions, deriving functional recurrence relations for boundary correlation functions using Coulomb gas methods.

Contribution

It introduces the boundary ground ring in Liouville quantum gravity with boundary cosmological constant and derives new functional recurrence equations for boundary correlators.

Findings

Derived boundary ground ring relations in Liouville quantum gravity.

Established functional recurrence equations for boundary correlation functions.

Connected boundary parameters with target space momenta shifts.

Abstract

We construct the boundary ground ring in c < 1 open string theories with non-zero boundary cosmological constant (FZZT brane), using the Coulomb gas representation. The ring relations yield an over-determined set of functional recurrence equations for the boundary correlation functions, which involve shifts of the target space momenta of the boundary fields as well as the boundary parameters on the different segments of the boundary.