Holonomies of gauge fields in twistor space 3: gravity as a square of N=4 theory

TL;DR

This paper presents a new formulation of gravitational holonomy operators in twistor space, expressing gravity as a square of N=4 theory, which includes spin-0 particles and supports quantum gravity models.

Contribution

It introduces an alternative gravitational holonomy operator as a square of N=4 holonomy, expanding the scope of amplitudes to include spin-0 particles.

Findings

New expression for gravitational holonomy as a square of N=4 holonomy

Inclusion of spin-0 massless particles in amplitudes

Support for squared models as quantum gravity theories

Abstract

In a recent paper, we show that an S-matrix functional for graviton amplitudes can be described by an N=8 supersymmetric gravitational holonomy operator in twistor space. In this paper, we obtain an alternative expression for the gravitational holonomy operator such that it can be interpreted as a square of an N=4 holonomy operator for frame fields, by taking a sum of certain shuffles over ordered indices. The new expression leads to amplitudes of not only spin-2 gravitons but also spin-0 massless particles. We discuss that the squared model is favored as a theory of quantum gravity.