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

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 Poincaré 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.

38 pages; v2. reference added + minor changes; v3. published version; v4. minor changes

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Cited by in corpus (7)

• Twistor Strings for N=8 Supergravity
• Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes
• Holonomies of gauge fields in twistor space 3: gravity as a square of N=4 theory
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes
• Holonomies of gauge fields in twistor space 5: amplitudes of gluons and massive scalars
• A Celestial Description of Planar Super-Yang-Mills Theory
• Holonomies of gauge fields in twistor space 6: incorporation of massive fermions