From twistors to twisted geometries

TL;DR

This paper explores the geometric origins of the phase space in loop quantum gravity, demonstrating how twistors can be used to understand twisted geometries that describe discrete spatial structures.

Contribution

It introduces a geometric interpretation of twistors to explain the phase space parametrization in loop quantum gravity, linking twistors to twisted geometries.

Findings

Phase space parametrized by twisted geometries

Geometric interpretation of twistors

Connection between twistors and discrete geometry

Abstract

In a previous paper we showed that the phase space of loop quantum gravity on a fixed graph can be parametrized in terms of twisted geometries, quantities describing the intrinsic and extrinsic discrete geometry of a cellular decomposition dual to the graph. Here we unravel the origin of the phase space from a geometric interpretation of twistors.