Twistors, CFT and Holography

TL;DR

This paper explores the quantization of twistor space, leading to a non-commutative geometric framework that connects to conformal field theory and holography, offering new insights into bulk/boundary dualities.

Contribution

It introduces a novel approach to quantizing twistors, resulting in a non-commutative geometry framework linked to CFT and holography, enhancing understanding of dualities.

Findings

Twistors can be quantized into operators in a Hilbert space.

Spacetime points emerge from twistor incidence relations as operators.

The resulting non-commutative geometry relates to conformal field theory and holography.

Abstract

According to one of many equivalent definitions of twistors a (null) twistor is a null geodesic in Minkowski spacetime. Null geodesics can intersect at points (events). The idea of Penrose was to think of a spacetime point as a derived concept: points are obtained by considering the incidence of twistors. One needs two twistors to obtain a point. Twistor is thus a ``square root'' of a point. In the present paper we entertain the idea of quantizing the space of twistors. Twistors, and thus also spacetime points become operators acting in a certain Hilbert space. The algebra of functions on spacetime becomes an operator algebra. We are therefore led to the realm of non-commutative geometry. This non-commutative geometry turns out to be related to conformal field theory and holography. Our construction sheds an interesting new light on bulk/boundary dualities.