Holonomies of gauge fields in twistor space 2: Hecke algebra, diffeomorphism, and graviton amplitudes

TL;DR

This paper introduces a novel gauge theory of gravity in twistor space using a gravitational holonomy operator, connecting algebraic structures to spacetime symmetries and graviton amplitudes, offering new insights into quantum gravity.

Contribution

It constructs a gravitational holonomy operator in twistor space with a Chan-Paton factor involving Poincaré and Iwahori-Hecke algebras, linking algebraic structures to gravitational symmetries.

Findings

Gravitational S-matrix functional expressed via supersymmetric holonomy operator

Invariance under spacetime translations and diffeomorphisms demonstrated

New algebraic framework for quantum gravity and cosmology proposed

Abstract

We define a theory of gravity by constructing a gravitational holonomy operator in twistor space. The theory is a gauge theory whose Chan-Paton factor is given by a trace over elements of Poincar\'{e} algebra and Iwahori-Hecke algebra. This corresponds to a fact that, in a spinor-momenta formalism, gravitational theories are invariant under spacetime translations and diffeomorphism. The former symmetry is embedded in tangent spaces of frame fields while the latter is realized by a braid trace. We make a detailed analysis on the gravitational Chan-Paton factor and show that an S-matrix functional for graviton amplitudes can be expressed in terms of a supersymmetric version of the holonomy operator. This formulation will shed a new light on studies of quantum gravity and cosmology in four dimensions.