The null identities for boundary operators in the $(2,2p+1)$ minimal gravity

TL;DR

This paper demonstrates that correlation numbers of boundary changing operators in certain minimal gravity models satisfy null identities, linking them to boundary preserving operators and revealing implications for boundary interactions.

Contribution

It introduces null identities for boundary changing operators in $(2,2p+1)$ minimal Liouville gravity, providing a new way to relate different boundary correlation functions.

Findings

Correlation numbers satisfy null identities.

Boundary changing operators can be expressed via boundary preserving operators.

Implications for boundary interactions in minimal gravity.

Abstract

By using the matrix-model representation, we show that correlation numbers of boundary changing operators (BCO) in $(2,2p+1)$ minimal Liouville gravity satisfy some identities, which we call the null identities. These identities enable us to express the correlation numbers of BCO in terms of those of boundary preserving operators. We also discuss a physical implication of the null identities as the manifestation of the boundary interaction.