# SO*(2N) coherent states for loop quantum gravity

## TL;DR

This paper introduces SO*(2N) coherent states in loop quantum gravity, revealing a new symmetry structure in the intertwiner space and exploring their semi-classical properties, extending previous U(N) symmetry work.

## Contribution

It demonstrates that the intertwiner Hilbert space admits a representation of SO*(2N) and constructs associated coherent states, advancing understanding of symmetries in loop quantum gravity.

## Key findings

- SO*(2N) acts on the intertwiner space
- Constructed Perelomov coherent states for SO*(2N)
- Semi-classical limit analysis reveals subtlety

## Abstract

A SU(2) intertwiner with N legs can be interpreted as the quantum state of a convex polyhedron with N faces (when working in 3d). We show that the intertwiner Hilbert space carries a representation of the non-compact group SO*(2N). This group can be viewed as the subgroup of the symplectic group Sp(4N,R) which preserves the SU(2) invariance. We construct the associated Perelomov coherent states and discuss the notion of semi-classical limit, which is more subtle that we could expect. Our work completes the work by Freidel and Livine which focused on the U(N) subgroup of SO*(2N).