文摘
In a recent paper, we show that an S-matrix functional for graviton amplitudes can be described by an 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 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.