# Boundary Kinematic Space

## TL;DR

This paper extends the concept of kinematic space to boundary conformal field theories, establishing a new dual gravitational representation and demonstrating how it can be used to reconstruct bulk geometry, thus broadening the understanding of bulk physics.

## Contribution

It introduces a boundary-specific kinematic space and a dual gravitational description, enabling bulk geometry reconstruction from boundary operator data.

## Key findings

- Boundary kinematic space identified as a subspace of full kinematic space.
- Representation of boundary OPE blocks in dual gravity established.
- Bulk geometry can be reconstructed using the new kinematic dictionary.

## Abstract

We extend kinematic space to a simple scenario where the state is not fixed by conformal invariance: the vacuum of a conformal field theory with a boundary (bCFT). We identify the kinematic space associated with the boundary operator product expansion (bOPE) as a subspace of the full kinematic space. In addition, we establish representations of the corresponding bOPE blocks in a dual gravitational description. We show how the new kinematic dictionary and the dynamical data in bOPE allows one to reconstruct the bulk geometry. This is evidence that kinematic space may be a useful construction for understanding bulk physics beyond just kinematics.