# Higher Equations of Motion in Boundary Liouville Field Theory

## TL;DR

This paper discovers an infinite set of boundary operator relations in boundary Liouville field theory, extending the bulk equations of motion, with potential implications for minimal boundary Liouville gravity.

## Contribution

It introduces boundary higher equations of motion linked to Virasoro singular representations, expanding the theoretical framework of boundary Liouville theory.

## Key findings

- Infinite boundary operator relations found
- Relations correspond to Virasoro singular representations
- Potential applications in boundary Liouville gravity

## Abstract

In addition to the ordinary bulk higher equations of motion in the boundary version of the Liouville conformal field theory, an infinite set of relations containing the boundary operators is found. These equations are in one-to-one correspondence with the singular representations of the Virasoro algebra. We comment on the possible applications in the context of minimal boundary Liouville gravity.