Minimal covariant quantum space-time

TL;DR

This paper introduces a minimal covariant quantum space-time model derived from the doubleton representation of ra9(4,2), interpretable as a quantized twistor space with potential implications for a ghost-free kk model.

Contribution

It presents a new minimal covariant quantum space-time framework based on the doubleton representation, with a semi-classical interpretation as quantized twistor space and implications for quantum gravity models.

Findings

Defines minimal covariant quantum space-time via generators and relations.

Shows the space admits a semi-classical interpretation as quantized twistor space.

Constructs over-complete coherent states with hierarchical uncertainty and curvature scales.

Abstract

We discuss minimal covariant quantum space-time ${\cal M}^{1,3}_0$, which is defined through the minimal doubleton representation of $\mathfrak{so}(4,2)$. An elementary definition in terms of generators and relations is given. This space is shown to admit a semi-classical interpretation as quantized twistor space ${\mathbb C} P^{1,2}$, viewed as a quantized $S^2$-bundle over a 3+1-dimensional $k=-1$ FLRW space-time. In particular we find an over-complete set of (quasi-) coherent states, with a large hierarchy between the uncertainty scale and the geometric curvature scale. This provides an interesting background for the IKKT model, leading to a $\mathfrak{hs}$-extended gravitational gauge theory, which is free of ghosts due to the constraints on phase space arising from the doubleton representation.