Twistor relative locality

TL;DR

This paper introduces a novel approach to relative locality using twistor space geometry, proposing a deformation of twistor theory where spacetime locality emerges and is affected by a non-flat connection, aligning with quantum gravity ideas.

Contribution

It develops a new framework linking twistor geometry with relative locality, providing a geometric model for quantum gravity effects on spacetime causality.

Findings

Locality in spacetime emerges from twistor bundle geometry.

Non-flat connections deform the notion of interactions in spacetime.

The approach maintains causality and relativistic invariance under deformation.

Abstract

We present a version of relative locality based on the geometry of twistor space. This can also be thought of as a new kind of deformation of twistor theory based on the construction of a bundle of twistor spaces over momentum space. Locality in space-time is emergent and is deformed in a precise way when a connection on that bundle is non-flat. This gives a precise and controlled meaning to Penrose's hypothesis that quantum gravity effects will deform twistor space in such a way as to maintain causality and relativistic invariance while weakening the notion that interactions take place at points in spacetime.